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  • 1.
    Abbas, Qaisar
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Weak Boundary and Interface Procedures for Wave and Flow Problems2011Doctoral thesis, monograph (Other academic)
    Abstract [en]

    In this thesis, we have analyzed the accuracy and stability aspects of weak boundary and interface conditions (WBCs) for high order finite difference methods on Summations-By-Parts (SBP) form. The numerical technique has been applied to wave propagation and flow problems.

    The advantage of WBCs over strong boundary conditions is that stability of the numerical scheme can be proven. The boundary procedures in the advection-diffusion equation for a boundary layer problem is analyzed. By performing Navier-Stokes calculations, it is shown that most of the conclusions from the model problem carries over to the fully nonlinear case.

    The work was complemented to include the new idea of using WBCs on multiple grid points in a region, where the data is known, instead of at a single point. It was shown that we can achieve high accuracy, an increased rate of convergence to steady-state and non-reflecting boundary conditions by using this approach.

    Using the SBP technique and WBCs, we have worked out how to construct conservative and energy stable hybrid schemes for shocks using two different approaches. In the first method, we combine a high order finite difference scheme with a second order MUSCL scheme. In the second method, a procedure to locally change the order of accuracy of the finite difference schemes is developed. The main purpose is to obtain a higher order accurate scheme in smooth regions and a low order non-oscillatory scheme in the vicinity of shocks.

    Furthermore, we have analyzed the energy stability of the MUSCL scheme, by reformulating the scheme in the framework of SBP and artificial dissipation operators. It was found that many of the standard slope limiters in the MUSCL scheme do not lead to a negative semi-definite dissipation matrix, as required to get pointwise stability.

    Finally, high order simulations of shock diffracting over a convex wall with two facets were performed. The numerical study is done for a range of Reynolds numbers. By monitoring the velocities at the solid wall, it was shown that the computations were resolved in the boundary layer. Schlieren images from the computational results were obtained which displayed new interesting flow features.

  • 2.
    Abbas, Qaisar
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Weak versus strong no-slip boundary conditions for the Navier-Stokes equations2010In: Engineering Applications of Computational Fluid Mechanics, ISSN 1994-2060, Vol. 4, p. 29-38Article in journal (Refereed)
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  • 3.
    Abbas, Qaisar
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Weak versus Strong No-Slip Boundary Conditions for the Navier-Stokes Equations2008In: Proc. 6th South African Conference on Computational and Applied Mechanics, South African Association for Theoretical and Applied Mechanics , 2008, p. 52-62Conference paper (Other academic)
  • 4.
    Abbas, Qaisar
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    van der Weide, Edwin
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Accurate and stable calculations involving shocks using a new hybrid scheme2009In: Proc. 19th AIAA CFD Conference, AIAA , 2009Conference paper (Refereed)
  • 5.
    Abbas, Qaisar
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    van der Weide, Edwin
    Faculty of Engineering Technology, University of Twente, AE Enschede, The Netherlands.
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Energy Stability of the MUSCL Scheme2010In: Proc. 7th South African Conference on Computational and Applied Mechanics, South African Association for Theoretical and Applied Mechanics , 2010, p. 65:1-8Conference paper (Other academic)
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  • 6.
    Abbas, Qaisar
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    van der Weide, Edwin
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Energy stability of the MUSCL scheme2010In: Numerical Mathematics and Advanced Applications: 2009, Berlin: Springer-Verlag , 2010, p. 61-68Conference paper (Refereed)
  • 7.
    Abdulla, Parosh Aziz
    et al.
    Uppsala Univ, Sweden.
    Atig, Mohamed Faouzi
    Uppsala Univ, Sweden.
    Chen, Yu-Fang
    Acad Sinica, Taiwan.
    Phi Diep, Bui
    Uppsala Univ, Sweden.
    Holik, Lukas
    Brno Univ Technol, Czech Republic.
    Rezine, Ahmed
    Linköping University, Department of Computer and Information Science, Software and Systems. Linköping University, Faculty of Science & Engineering.
    Rummer, Philipp
    Uppsala Univ, Sweden.
    TRAU : SMT solver for string constraints2018In: PROCEEDINGS OF THE 2018 18TH CONFERENCE ON FORMAL METHODS IN COMPUTER AIDED DESIGN (FMCAD), IEEE , 2018, p. 165-169Conference paper (Refereed)
    Abstract [en]

    We introduce TRAU, an SMT solver for an expressive constraint language, including word equations, length constraints, context-free membership queries, and transducer constraints. The satisfiability problem for such a class of constraints is in general undecidable. The key idea behind TRAU is a technique called flattening, which searches for satisfying assignments that follow simple patterns. TRAU implements a Counter-Example Guided Abstraction Refinement (CEGAR) framework which contains both an under- and an over-approximation module. The approximations are refined in an automatic manner by information flow between the two modules. The technique implemented by TRAU can handle a rich class of string constraints and has better performance than state-of-the-art string solvers.

  • 8.
    Abgrall, Remi
    et al.
    Institute of Mathematics, University of Zurich, Switzerland.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering. Department of Mathematics and Applied Mathematics, University of Johannesburg, South Africa.
    Öffner, Philipp
    Institute of Mathematics, University of Zurich, Switzerland. Institute of Mathematics, Johannes Gutenberg-Universtiy, Germany.
    Tokareva, Svetlana
    Theoretical Division, Applied Mathematics and Plasma Physics Group (T-5), Los Alamos National Laboratory, USA.
    Analysis of the SBP-SAT Stabilization for Finite Element Methods Part I: Linear Problems2020In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 85, no 2, article id 43Article in journal (Refereed)
    Abstract [en]

    In the hyperbolic community, discontinuous Galerkin (DG) approaches are mainly applied when finite element methods are considered. As the name suggested, the DG framework allows a discontinuity at the element interfaces, which seems for many researchers a favorable property in case of hyperbolic balance laws. On the contrary, continuous Galerkin methods appear to be unsuitable for hyperbolic problems and there exists still the perception that continuous Galerkin methods are notoriously unstable. To remedy this issue, stabilization terms are usually added and various formulations can be found in the literature. However, this perception is not true and the stabilization terms are unnecessary, in general. In this paper, we deal with this problem, but present a different approach. We use the boundary conditions to stabilize the scheme following a procedure that are frequently used in the finite difference community. Here, the main idea is to impose the boundary conditions weakly and specific boundary operators are constructed such that they guarantee stability. This approach has already been used in the discontinuous Galerkin framework, but here we apply it with a continuous Galerkin scheme. No internal dissipation is needed even if unstructured grids are used. Further, we point out that we do not need exact integration, it suffices if the quadrature rule and the norm in the differential operator are the same, such that the summation-by-parts property is fulfilled meaning that a discrete Gauss Theorem is valid. This contradicts the perception in the hyperbolic community that stability issues for pure Galerkin scheme exist. In numerical simulations, we verify our theoretical analysis.

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  • 9. Order onlineBuy this publication >>
    Achieng, Pauline
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Analysis of the Robin-Dirichlet iterative procedure for solving the Cauchy problem for elliptic equations with extension to unbounded domains2020Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    In this thesis we study the Cauchy problem for elliptic equations. It arises in many areas of application in science and engineering as a problem of reconstruction of solutions to elliptic equations in a domain from boundary measurements taken on a part of the boundary of this domain. The Cauchy problem for elliptic equations is known to be ill-posed.

    We use an iterative regularization method based on alternatively solving a sequence of well-posed mixed boundary value problems for the same elliptic equation. This method, based on iterations between Dirichlet-Neumann and Neumann-Dirichlet mixed boundary value problems was first proposed by Kozlov and Maz’ya [13] for Laplace equation and Lame’ system but not Helmholtz-type equations. As a result different modifications of this original regularization method have been proposed in literature. We consider the Robin-Dirichlet iterative method proposed by Mpinganzima et.al [3] for the Cauchy problem for the Helmholtz equation in bounded domains.

    We demonstrate that the Robin-Dirichlet iterative procedure is convergent for second order elliptic equations with variable coefficients provided the parameter in the Robin condition is appropriately chosen. We further investigate the convergence of the Robin-Dirichlet iterative procedure for the Cauchy problem for the Helmholtz equation in a an unbounded domain. We derive and analyse the necessary conditions needed for the convergence of the procedure.

    In the numerical experiments, the precise behaviour of the procedure for different values of k2 in the Helmholtz equation is investigated and the results show that the speed of convergence depends on the choice of the Robin parameters, μ0 and μ1. In the unbounded domain case, the numerical experiments demonstrate that the procedure is convergent provided that the domain is truncated appropriately and the Robin parameters, μ0 and μ1 are also chosen appropriately.

    List of papers
    1. Analysis of Dirichlet–Robin Iterations for Solving the Cauchy Problem for Elliptic Equations
    Open this publication in new window or tab >>Analysis of Dirichlet–Robin Iterations for Solving the Cauchy Problem for Elliptic Equations
    2021 (English)In: Bulletin of the Iranian Mathematical Society, ISSN 1735-8515, Vol. 47, p. 1681-1699Article in journal (Refereed) Published
    Abstract [en]

    The Cauchy problem for general elliptic equations of second order is considered. In a previous paper (Berntsson et al. in Inverse Probl Sci Eng 26(7):1062–1078, 2018), it was suggested that the alternating iterative algorithm suggested by Kozlov and Maz’ya can be convergent, even for large wavenumbers k2, in the Helmholtz equation, if the Neumann boundary conditions are replaced by Robin conditions. In this paper, we provide a proof that shows that the Dirichlet–Robin alternating algorithm is indeed convergent for general elliptic operators provided that the parameters in the Robin conditions are chosen appropriately. We also give numerical experiments intended to investigate the precise behaviour of the algorithm for different values of k2 in the Helmholtz equation. In particular, we show how the speed of the convergence depends on the choice of Robin parameters.

    Place, publisher, year, edition, pages
    Springer, 2021
    Keywords
    Helmholtz equation, Cauchy problem, Inverse problem, Ill-posed problem
    National Category
    Mathematical Analysis
    Identifiers
    urn:nbn:se:liu:diva-170834 (URN)10.1007/s41980-020-00466-7 (DOI)000575739300001 ()2-s2.0-85092146699 (Scopus ID)
    Available from: 2020-10-26 Created: 2020-10-26 Last updated: 2024-02-22Bibliographically approved
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  • 10. Order onlineBuy this publication >>
    Achieng, Pauline
    Linköping University, Department of Mathematics, Analysis and Mathematics Education. Linköping University, Faculty of Science & Engineering.
    Reconstruction of solutions of Cauchy problems for elliptic equations in bounded and unbounded domains using iterative regularization methods2023Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Cauchy problems for elliptic equations arise in applications in science and engineering. These problems often involve finding important information about an elliptical system from indirect or incomplete measurements. Cauchy problems for elliptic equations are known to be disadvantaged in the sense that a small pertubation in the input can result in a large error in the output. Regularization methods are usually required in order to be able to find stable solutions. In this thesis we study the Cauchy problem for elliptic equations in both bounded and unbounded domains using iterative regularization methods. In Paper I and II, we focus on an iterative regularization technique which involves solving a sequence of mixed boundary value well-posed problems for the same elliptic equation. The original version of the alternating iterative technique is based on iterations alternating between Dirichlet-Neumann and Neumann-Dirichlet boundary value problems. This iterative method is known to possibly work for Helmholtz equation. Instead we study a modified version based on alternating between Dirichlet-Robin and Robin-Dirichlet boundary value problems. First, we study the Cauchy problem for general elliptic equations of second order with variable coefficients in a limited domain. Then we extend to the case of unbounded domains for the Cauchy problem for Helmholtz equation. For the Cauchy problem, in the case of general elliptic equations, we show that the iterative method, based on Dirichlet-Robin, is convergent provided that parameters in the Robin condition are chosen appropriately. In the case of an unbounded domain, we derive necessary, and sufficient, conditions for convergence of the Robin-Dirichlet iterations based on an analysis of the spectrum of the Laplacian operator, with boundary conditions of Dirichlet and Robin types.

    In the numerical tests, we investigate the precise behaviour of the Dirichlet-Robin iterations, for different values of the wave number in the Helmholtz equation, and the results show that the convergence rate depends on the choice of the Robin parameter in the Robin condition. In the case of unbounded domain, the numerical experiments show that an appropriate truncation of the domain and an appropriate choice of Robin parameter in the Robin condition lead to convergence of the Robin-Dirichlet iterations.

    In the presence of noise, additional regularization techniques have to implemented for the alternating iterative procedure to converge. Therefore, in Paper III and IV we focus on iterative regularization methods for solving the Cauchy problem for the Helmholtz equation in a semi-infinite strip, assuming that the data contains measurement noise. In addition, we also reconstruct a radiation condition at infinity from the given Cauchy data. For the reconstruction of the radiation condition, we solve a well-posed problem for the Helmholtz equation in a semi-infinite strip. The remaining solution is obtained by solving an ill-posed problem. In Paper III, we consider the ordinary Helmholtz equation and use seperation of variables to analyze the problem. We show that the radiation condition is described by a non-linear well-posed problem that provides a stable oscillatory solution to the Cauchy problem. Furthermore, we show that the ill–posed problem can be regularized using the Landweber’s iterative method and the discrepancy principle. Numerical tests shows that the approach works well.

    Paper IV is an extension of the theory from Paper III to the case of variable coefficients. Theoretical analysis of this Cauchy problem shows that, with suitable bounds on the coefficients, can iterative regularization methods be used to stabilize the ill-posed Cauchy problem.

    List of papers
    1. Analysis of Dirichlet–Robin Iterations for Solving the Cauchy Problem for Elliptic Equations
    Open this publication in new window or tab >>Analysis of Dirichlet–Robin Iterations for Solving the Cauchy Problem for Elliptic Equations
    2021 (English)In: Bulletin of the Iranian Mathematical Society, ISSN 1735-8515, Vol. 47, p. 1681-1699Article in journal (Refereed) Published
    Abstract [en]

    The Cauchy problem for general elliptic equations of second order is considered. In a previous paper (Berntsson et al. in Inverse Probl Sci Eng 26(7):1062–1078, 2018), it was suggested that the alternating iterative algorithm suggested by Kozlov and Maz’ya can be convergent, even for large wavenumbers k2, in the Helmholtz equation, if the Neumann boundary conditions are replaced by Robin conditions. In this paper, we provide a proof that shows that the Dirichlet–Robin alternating algorithm is indeed convergent for general elliptic operators provided that the parameters in the Robin conditions are chosen appropriately. We also give numerical experiments intended to investigate the precise behaviour of the algorithm for different values of k2 in the Helmholtz equation. In particular, we show how the speed of the convergence depends on the choice of Robin parameters.

    Place, publisher, year, edition, pages
    Springer, 2021
    Keywords
    Helmholtz equation, Cauchy problem, Inverse problem, Ill-posed problem
    National Category
    Mathematical Analysis
    Identifiers
    urn:nbn:se:liu:diva-170834 (URN)10.1007/s41980-020-00466-7 (DOI)000575739300001 ()2-s2.0-85092146699 (Scopus ID)
    Available from: 2020-10-26 Created: 2020-10-26 Last updated: 2024-02-22Bibliographically approved
    2. Robin-Dirichlet alternating iterative procedure for solving the Cauchy problem for Helmholtz equation in an unbounded domain
    Open this publication in new window or tab >>Robin-Dirichlet alternating iterative procedure for solving the Cauchy problem for Helmholtz equation in an unbounded domain
    2023 (English)In: Journal of Inverse and Ill-Posed Problems, ISSN 0928-0219, E-ISSN 1569-3945Article in journal (Refereed) Epub ahead of print
    Abstract [en]

    We consider the Cauchy problem for the Helmholtz equation with a domain in with N cylindrical outlets to infinity with bounded inclusions in . Cauchy data are prescribed on the boundary of the bounded domains and the aim is to find solution on the unbounded part of the boundary. In 1989, Kozlov and Mazya proposed an alternating iterative method for solving Cauchy problems associated with elliptic, selfadjoint and positive-definite operators in bounded domains. Different variants of this method for solving Cauchy problems associated with Helmholtz-type operators exists. We consider the variant proposed by Berntsson, Kozlov, Mpinganzima and Turesson (2018) for bounded domains and derive the necessary conditions for the convergence of the procedure in unbounded domains. For the numerical implementation, a finite difference method is used to solve the problem in a simple rectangular domain in R-2 that represent a truncated infinite strip. The numerical results shows that by appropriate truncation of the domain and with appropriate choice of the Robin parameters mu(0) and mu(1), the Robin-Dirichlet alternating iterative procedure is convergent.

    Place, publisher, year, edition, pages
    WALTER DE GRUYTER GMBH, 2023
    Keywords
    Helmholtz equation; Cauchy problem; inverse problem ill-posed problem
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:liu:diva-192481 (URN)10.1515/jiip-2020-0133 (DOI)000940871600001 ()
    Available from: 2023-03-21 Created: 2023-03-21 Last updated: 2023-11-13
    3. Reconstruction of the Radiation Condition and Solution for the Helmholtz Equation in a Semi-infinite Strip from Cauchy Data on an Interior Segment
    Open this publication in new window or tab >>Reconstruction of the Radiation Condition and Solution for the Helmholtz Equation in a Semi-infinite Strip from Cauchy Data on an Interior Segment
    2023 (English)In: Computational Methods in Applied Mathematics, ISSN 1609-4840, E-ISSN 1609-9389Article in journal (Refereed) Epub ahead of print
    Abstract [en]

    We consider an inverse problem for the Helmholtz equation of reconstructing a solution from measurements taken on a segment inside a semi-infinite strip. Homogeneous Neumann conditions are prescribed on both side boundaries of the strip and an unknown Dirichlet condition on the remaining part of the boundary. Additional complexity is that the radiation condition at infinity is unknown. Our aim is to find the unknown function in the Dirichlet boundary condition and the radiation condition. Such problems appear in acoustics to determine acoustical sources and surface vibrations from acoustic field measurements. The problem is split into two sub-problems, a well-posed and an ill-posed problem. We analyse the theoretical properties of both problems; in particular, we show that the radiation condition is described by a stable non-linear problem. The second problem is ill-posed, and we use the Landweber iteration method together with the discrepancy principle to regularize it. Numerical tests show that the approach works well.

    Place, publisher, year, edition, pages
    WALTER DE GRUYTER GMBH, 2023
    Keywords
    Helmholtz Equation; Inverse Problem; Cauchy Problem; Ill-Posed Problem; Well-Posed Problem; Landweber Method
    National Category
    Fluid Mechanics and Acoustics
    Identifiers
    urn:nbn:se:liu:diva-196637 (URN)10.1515/cmam-2022-0244 (DOI)001035412500001 ()
    Available from: 2023-08-17 Created: 2023-08-17 Last updated: 2023-11-13
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  • 11.
    Achieng, Pauline
    et al.
    Linköping University, Department of Mathematics, Analysis and Mathematics Education. Linköping University, Faculty of Science & Engineering. Univ Nairobi, Kenya.
    Berntsson, Fredrik
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Kozlov, Vladimir
    Linköping University, Department of Mathematics, Analysis and Mathematics Education. Linköping University, Faculty of Science & Engineering.
    Robin-Dirichlet alternating iterative procedure for solving the Cauchy problem for Helmholtz equation in an unbounded domain2023In: Journal of Inverse and Ill-Posed Problems, ISSN 0928-0219, E-ISSN 1569-3945Article in journal (Refereed)
    Abstract [en]

    We consider the Cauchy problem for the Helmholtz equation with a domain in with N cylindrical outlets to infinity with bounded inclusions in . Cauchy data are prescribed on the boundary of the bounded domains and the aim is to find solution on the unbounded part of the boundary. In 1989, Kozlov and Mazya proposed an alternating iterative method for solving Cauchy problems associated with elliptic, selfadjoint and positive-definite operators in bounded domains. Different variants of this method for solving Cauchy problems associated with Helmholtz-type operators exists. We consider the variant proposed by Berntsson, Kozlov, Mpinganzima and Turesson (2018) for bounded domains and derive the necessary conditions for the convergence of the procedure in unbounded domains. For the numerical implementation, a finite difference method is used to solve the problem in a simple rectangular domain in R-2 that represent a truncated infinite strip. The numerical results shows that by appropriate truncation of the domain and with appropriate choice of the Robin parameters mu(0) and mu(1), the Robin-Dirichlet alternating iterative procedure is convergent.

  • 12.
    Adib Yaghmaie, Farnaz
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering. Nanyang Technol Univ, Singapore.
    Movric, Kristian Hengster
    Czech Tech Univ, Czech Republic.
    Lewis, Frank L.
    Univ Texas Arlington, TX 76019 USA; Northeastern Univ, Peoples R China.
    Su, Rong
    Nanyang Technol Univ, Singapore.
    Differential graphical games for H-infinity control of linear heterogeneous multiagent systems2019In: International Journal of Robust and Nonlinear Control, ISSN 1049-8923, E-ISSN 1099-1239, Vol. 29, no 10, p. 2995-3013Article in journal (Refereed)
    Abstract [en]

    Differential graphical games have been introduced in the literature to solve state synchronization problem for linear homogeneous agents. When the agents are heterogeneous, the previous notion of graphical games cannot be used anymore and a new definition is required. In this paper, we define a novel concept of differential graphical games for linear heterogeneous agents subject to external unmodeled disturbances, which contain the previously introduced graphical game for homogeneous agents as a special case. Using our new formulation, we can solve both the output regulation and H-infinity output regulation problems. Our graphical game framework yields coupled Hamilton-Jacobi-Bellman equations, which are, in general, impossible to solve analytically. Therefore, we propose a new actor-critic algorithm to solve these coupled equations numerically in real time. Moreover, we find an explicit upper bound for the overall L2-gain of the output synchronization error with respect to disturbance. We demonstrate our developments by a simulation example.

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  • 13.
    Adlers, Mikael
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Topics in Sparse Least Squares Problems2000Doctoral thesis, monograph (Other academic)
    Abstract [en]

    This thesis addresses topics in sparse least squares computation. A stable method for solving the least squares problem, min ||Ax-b||2 is based on the QR factorization.Here we have addressed the difficulty for storing the orthogonal matrix Q. Using traditional methods, the number of nonzero elements in Q makes it in many cases not feasible to store. Using the multifrontal technique when computing the QR factorization,Q may be stored and used more efficiently. A new user friendly Matlab implementation is developed.

    When a row in A is dense the factor R from the QR factorization may be completely dense. Therefore problems with dense rows must be treated by special techniques. The usual way to handle dense rows is to partition the problem into one sparse and one dense subproblem. The drawback with this approach is that the sparse subproblem may be more ill-conditioned than the original problem or even not have a unique solution. Another method, useful for problems with few dense rows, is based on matrix stretching, where the dense rows are split into several less dense rows linked then together with new artificial variables. We give and analyze the conditioning of the matrix obtained by this method and show that no ill-conditioned subproblem arise.

    In many least squares problems upper and lower bounds on the variables have to be satisfied at the solution. This type of problem arises, for example, in reconstruction problems in geodesy and tomography. Here methods based on direct factorization methods for sparse matrix computation are explored. Two completely different approaches for solving the problem are discussed and compared, i.e. active set methods and primal-dual interior-point methods based on Mehrotra's predictor-corrector path following method. An active set block method suitable for sparse problems is developed and a convergence proof is presented. The choice of barrier parameter, multiple corrections and finite termination for the interior-point method are discussed. Numerical comparison is given of the active set method, the interior-point method, together with an trust region method based on the interior-reflective Newton implemented in the optimization toolbox for MATLAB. The numerical tests show that the block active set method is faster and gives better accuracy for both nondegenerate and degenerate problems.

  • 14.
    Alacaoglu, Ahmet
    et al.
    Ecole Polytech Fed Lausanne EPFL, Switzerland.
    Malitskyi, Yurii
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Cevher, Volkan
    Ecole Polytech Fed Lausanne EPFL, Switzerland.
    Forward-reflected-backward method with variance reduction2021In: Computational optimization and applications, ISSN 0926-6003, E-ISSN 1573-2894, Vol. 80, no 2, p. 321-346Article in journal (Refereed)
    Abstract [en]

    We propose a variance reduced algorithm for solving monotone variational inequalities. Without assuming strong monotonicity, cocoercivity, or boundedness of the domain, we prove almost sure convergence of the iterates generated by the algorithm to a solution. In the monotone case, the ergodic average converges with the optimal O(1/k) rate of convergence. When strong monotonicity is assumed, the algorithm converges linearly, without requiring the knowledge of strong monotonicity constant. We finalize with extensions and applications of our results to monotone inclusions, a class of non-monotone variational inequalities and Bregman projections.

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  • 15.
    Alfredsson, Lars-Inge
    lasse.alfredsson@liu.se.
    VLSI Architectures and Arithmetic Operations with Application to the Fermat Number Transform1996Doctoral thesis, monograph (Other academic)
    Abstract [en]

    The properties of arithmetic operations in Fermat integer quotient rings 2m+1, where m = 2t, are investigated. The arithmetic operations considered are mainly those involved in the computation of the Fermat number transform. We consider some ways of representing the binary coded integers in such rings and investigate VLSI architectures for arithmetic operations, with respect to the different element representations. The VLSI architectures are mutually compared with respect to area (A) and time (T) complexity and area-time performance (AT2). The VLSI model chosen is a linears witch-level RC model.

    In the polar representation, the nonzero elements of a field are represented by the powers of a primitive element of the field. In the thesis we particularly investigate the properties of arithmetic operations and their corresponding VLSI architectureswith respect to the polar representation of the elements of Fermat prime fields. Somenew results regarding the applicability of the Fermat number transform when usingthe polar representation are also presented.

  • 16.
    Alskog, Måns
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Implementation of a Fast Approximation Algorithm for Precedence Constrained Scheduling2022Independent thesis Advanced level (degree of Master (Two Years)), 28 HE creditsStudent thesis
    Abstract [en]

    We present an implementation of a very recent approximation algorithm for scheduling jobs on a single machine with precedence constraints, minimising the total weighted completion time. We also evaluate the performance of this implementation. The algorithm was published by Shi Li in 2021 and is a (6+ε)-approximation algorithm for the multiprocessor problem P|prec|∑j wjCj. We have implemented a version which is a (2+ε)-approximation algorithm for the single processor problem 1|prec|∑j wjCj. This special case can easily be generalised to the multiprocessor case, as the two algorithms are based on the same LP relaxation of the problem. Unlike other approximation algorithms for this and similar problems, for example, those published by Hall, Schulz, Shmoys and Wein in 1997, and by Li in 2020, this algorithm has been developed with a focus on obtaining a good asymptotic run time guarantee, rather than obtaining the best possible guarantee on the quality of solutions. Li’s algorithm has run time O((n+κ) · polylog(n+κ) · log3 pmax · 1/ε2), where n is the number of jobs, κ is the number of precedence constraints and pmax is the largest of the processing times of the jobs. We also present a detailed explanation of the algorithm aimed at readers who do not necessarily have a background in scheduling and/or approximation algorithms, based on the paper by Li. Finally, we empirically evaluate how well (our implementation of) this algorithm performs in practice. The performance was measured on a set of 96 randomly generated instances, with the largest instance having 1024 jobs and 32 768 precedence constraints. We can find a solution for an instance with 512 jobs and 11 585 precedence constraints in 25 minutes.

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  • 17.
    Altafini, Claudio
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    The Geometric Phase of Stock Trading2016In: PLOS ONE, E-ISSN 1932-6203, Vol. 11, no 8, p. e0161538-Article in journal (Refereed)
    Abstract [en]

    Geometric phases describe how in a continuous-time dynamical system the displacement of a variable (called phase variable) can be related to other variables (shape variables) undergoing a cyclic motion, according to an area rule. The aim of this paper is to show that geometric phases can exist also for discrete-time systems, and even when the cycles in shape space have zero area. A context in which this principle can be applied is stock trading. A zero-area cycle in shape space represents the type of trading operations normally carried out by high-frequency traders (entering and exiting a position on a fast time-scale), while the phase variable represents the cash balance of a trader. Under the assumption that trading impacts stock prices, even zero-area cyclic trading operations can induce geometric phases, i.e., profits or losses, without affecting the stock quote.

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  • 18.
    Alvarez-Garcia, David
    et al.
    Univ Oviedo, Spain.
    Thornberg, Robert
    Linköping University, Department of Behavioural Sciences and Learning, Education, Teaching and Learning. Linköping University, Faculty of Educational Sciences.
    Suarez-Garcia, Zara
    Univ Oviedo, Spain.
    Validation of a Scale for Assessing Bystander Responses in Bullying2021In: Psicothema (Oviedo), ISSN 0214-9915, E-ISSN 1886-144X, Vol. 33, no 4, p. 623-630Article in journal (Refereed)
    Abstract [en]

    Background: This study sought to analyse the metric properties of the scores obtained with an adaptation of the Student Bystander Behaviour Scale (SBBS; Thornberg & Jungert, 2013) in Spanish primary-school students and to examine the types of responses students reported as witnesses to school bullying, along with their relationship to empathy. Method: The Spanish adaptation of the SBBS and a self-report questionnaire about empathy were given to 1108 primary-school students, aged 9-11 years old (48.4% girls) in Asturias (Spain). The students were from 29 schools, selected by simple random sampling from all of the primary schools in the region. Results: Exploratory and confirmatory factor analysis indicated that the adapted version, like the original SBBS, measured three types of witness response to school bullying: defender, passive, and pro-bully. Most students reported that they defended, or would defend, the victim. This trend was more marked in those who had not witnessed bullying. The type of response to bullying was related to empathy, positively with defender responses, and negatively with passive and pro-bully responses. Conclusions: The scores from the adapted version of the SBBS demonstrated metrics of reliability and validity suitable for identifying the type of response to school bullying from primary-school students.

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  • 19.
    Amsallem, David
    et al.
    Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305-4035, USA.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Energy Stable Model Reduction of Neurons by Non-negative Discrete Empirical Interpolation2016In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 38, no 2, p. B297-B326Article in journal (Refereed)
    Abstract [en]

    The accurate and fast prediction of potential propagation in neuronal networks is of prime importance in neurosciences. This work develops a novel structure-preserving model reduction technique to address this problem based on Galerkin projection and nonnegative operator approximation. It is first shown that the corresponding reduced-order model is guaranteed to be energy stable, thanks to both the structure-preserving approach that constructs a distinct reduced-order basis for each cable in the network and the preservation of nonnegativity. Furthermore, a posteriori error estimates are provided, showing that the model reduction error can be bounded and controlled. Finally, the application to the model reduction of a large-scale neuronal network underlines the capability of the proposed approach to accurately predict the potential propagation in such networks while leading to important speedups.

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  • 20.
    Amsallem, David
    et al.
    Department of Aeronautics and Astronautics, Stanford University, USA.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.
    High-order accurate difference schemes for the Hodgkin-Huxley equations2013In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 252, p. 573-590Article in journal (Refereed)
    Abstract [en]

    A novel approach for simulating potential propagation in neuronal branches with high accuracy is developed. The method relies on high-order accurate difference schemes using the Summation-By-Parts operators with weak boundary and interface conditions applied to the Hodgkin–Huxley equations. This work is the first demonstrating high accuracy for that equation. Several boundary conditions are considered including the non-standard one accounting for the soma presence, which is characterized by its own partial differential equation. Well-posedness for the continuous problem as well as stability of the discrete approximation is proved for all the boundary conditions. Gains in terms of CPU times are observed when high-order operators are used, demonstrating the advantage of the high-order schemes for simulating potential propagation in large neuronal trees.

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  • 21.
    Andersson Granberg, Tobias
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering.
    Optimized Dispatch of Fire and Rescue Resources2022In: COMPUTATIONAL LOGISTICS (ICCL 2022), SPRINGER INTERNATIONAL PUBLISHING AG , 2022, Vol. 13557, p. 132-146Conference paper (Refereed)
    Abstract [en]

    A dispatching problem for fire and rescue services is considered, where firefighters have to be allocated to vehicles, and vehicles dispatched to an emergency. A mathematical model for the problem is formulated, capable of managing multiple alarm plans for each emergency considered. The model is solved both exactly and heuristically, using input data from a fire and rescue service area in Skane, Sweden. The results show that the exact solution method might be too time consuming in some cases, but that the heuristic in most cases finds the optimal solution.

  • 22.
    Andersson Granberg, Tobias
    et al.
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, The Institute of Technology.
    Norin, Anna
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, The Institute of Technology.
    Värbrand, Peter
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, The Institute of Technology.
    Yuan, Di
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, The Institute of Technology.
    Integrating optimization and simulation to gain more efficient airport logistics2009In: Eighth USA/Europe Air Traffic Management Research and Development Seminar (ATM2009), 2009, p. 1-10Conference paper (Refereed)
    Abstract [en]

    In this paper we present airport logistics, which is a framework of resource management in the air transportation system. Focus is on the processes supporting turn-around. A detailed simulation model of various processes involved in turn-around is developed, by which the interaction between these processes are analyzed. We show that integrating optimization and simulation is a powerful tool to demonstrate efficiency improvements in airport logistics, using scheduling de-icing trucks as an example. An optimization algorithm for scheduling de-icing trucks is developed and simulations are performed comparing different schedules. The schedule obtained when considering total airport performance in the optimization algorithm gives minimum flight delay and waiting times in the simulations.

  • 23. Order onlineBuy this publication >>
    Andersson, Henrik
    Linköping University, Department of Science and Technology. Linköping University, The Institute of Technology.
    Coordinated Routing: applications in location and inventory management2006Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Almost everywhere, routing plays an important role in everyday life. This thesis consists of three parts, each studying different applications where routing decisions are coordinated with other decisions. A common denominator in all applications is that an intelligent utilization of a fleet of vehicles is crucial for the performance of the system. In the first part, routing and inventorymanagement decisions are coordinated, in the second part, routing decisions concerning different modes of transportation are coordinated with inventory management, and in the third part, location decision and routing are coordinated.

    In the first part, an application concerning waste management is presented. Many industries generate garbage, and instead of handling the waste disposal themselves, other companies, specialized in garbage collection, handle the disposal. Each industry rents containers from a company to be used for waste, and the garbage collection companies handle the collection. The industries buy a service including one or more containers at the industry and the garbage collection companies are obliged to make sure that the containers never become overfull. The idea is that the industries buy this service and in return, the garbage collection company can plan the collection so that the overall cost and the number of overfull containers is minimized. Two models for the problem facing the garbage collection company are proposed. The first is solved using a Lagrangean relaxation approach on a flow based model, and the second is solved using Benders decomposition on a column based model.

    The second part investigates a distribution chain management problem taken from the Swedish pulp industry. Given fixed production plans at the mills, and fixed customer demands, the problem is to minimize the distribution cost. Unlike many other models for marine distribution chains, the customers are not located at the harbors. This means that the model proposed also incorporates the distribution planning from the harbors to the customers. All customers are not served from the harbors; some are served directly from the mills using trucks and trains to distribute the pulp, and these decisions are also included. The problem is modeled as a mixed integer linear program and solved using a branch and price scheme. Due to the complexity of the problem, the solution strategy is divided into two phases, where the first emphasizes the generation of schedules for the vessels operated by the company, while the second deals with the chartering of vessels on the spot market.

    In the third part, routing is combined with location decisions in the location-routing problem. Special emphasis is given to strategic management where decision makers must make location, capacity and routing decisions over a long planning period. The studied application comes fromstrategic schoolmanagement, where the location and capacity of the schools as well as their catchment areas are under consideration. The problem is modeled as a mixed integer linear program. The computational study shows the importance of incorporating

    a routing component allowing multiple visits, as well as the danger of having a too short planning period.

    List of papers
    1. A Lagrangean Based Heuristic for the Inventory Routing Problem
    Open this publication in new window or tab >>A Lagrangean Based Heuristic for the Inventory Routing Problem
    2006 (English)In: European Journal of Operational Research, ISSN 0377-2217Article in journal (Refereed) Submitted
    National Category
    Engineering and Technology
    Identifiers
    urn:nbn:se:liu:diva-13900 (URN)
    Available from: 2006-07-12 Created: 2006-07-12
    2. A pseudo Benders Decomposition Approach
    Open this publication in new window or tab >>A pseudo Benders Decomposition Approach
    2002 (English)In: Proceedings of Nordic MPS ’02, 2002Conference paper, Published paper (Other academic)
    National Category
    Engineering and Technology
    Identifiers
    urn:nbn:se:liu:diva-13901 (URN)
    Available from: 2006-07-12 Created: 2006-07-12
    3. A Distribution Chain Management Problem in the Swedish Pulp Industry
    Open this publication in new window or tab >>A Distribution Chain Management Problem in the Swedish Pulp Industry
    2006 (English)Article in journal (Refereed) Submitted
    National Category
    Engineering and Technology
    Identifiers
    urn:nbn:se:liu:diva-13902 (URN)
    Available from: 2006-07-12 Created: 2006-07-12
    4. Decision Support for Distribution Chain Management: the Swedish Pulp Industry
    Open this publication in new window or tab >>Decision Support for Distribution Chain Management: the Swedish Pulp Industry
    2004 (English)In: 7th International Conference on Intelligent Transport Systems, 2004, p. 1051-1056Conference paper, Published paper (Other academic)
    National Category
    Engineering and Technology
    Identifiers
    urn:nbn:se:liu:diva-13903 (URN)
    Available from: 2006-07-12 Created: 2006-07-12 Last updated: 2009-04-23
    5. Location-Routing Problems: An Annotated Bibliography
    Open this publication in new window or tab >>Location-Routing Problems: An Annotated Bibliography
    2006 (English)Article in journal (Refereed) Submitted
    National Category
    Engineering and Technology
    Identifiers
    urn:nbn:se:liu:diva-13904 (URN)
    Available from: 2006-07-12 Created: 2006-07-12
    6. The Relocation-Routing Problem
    Open this publication in new window or tab >>The Relocation-Routing Problem
    2006 (English)Article in journal (Refereed) Submitted
    National Category
    Engineering and Technology
    Identifiers
    urn:nbn:se:liu:diva-13905 (URN)
    Available from: 2006-07-12 Created: 2006-07-12
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  • 24.
    Andersson, Lars-Erik
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Pinto da Costa, A.
    University of Lisbon, Portugal.
    Agwa, M. A.
    Zagazig University, Egypt.
    Existence and uniqueness for frictional incremental and rate problems - sharp critical bounds2016In: Zeitschrift für angewandte Mathematik und Mechanik, ISSN 0044-2267, E-ISSN 1521-4001, Vol. 96, no 1, p. 78-105Article in journal (Refereed)
    Abstract [en]

    We investigate frictional contact problems for discrete linear elastic structures, in particular the quasistatic incremental problem and the rate problem. It is shown that sharp conditions on the coefficients of friction for unique solvability of these problems are the same. We also give explicit expressions of these critical bounds by using a method of optimization. For the case of two spatial dimensions the conditions are formulated as a huge set of non symmetric eigenvalue problem. A computer program for solving these problems was designed and used to compute the critical bounds for some structures of relative small size, some of which appeared in the literature. The results of a variety of numerical experiments with uniform and non uniform distributions of the frictional properties are presented. (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

  • 25.
    Andersson, Mats
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Burdakov, Oleg
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Zikrin, Spartak
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Global search strategies for solving multilinear least-squares problems2012In: Sultan Qaboos University Journal for Science, ISSN 1027-524X, Vol. 17, no 1, p. 12-21Article in journal (Refereed)
    Abstract [en]

    The multilinear least-squares (MLLS) problem is an extension of the linear leastsquares problem. The difference is that a multilinear operator is used in place of a matrix-vector product. The MLLS is typically a large-scale problem characterized by a large number of local minimizers. It originates, for instance, from the design of filter networks. We present a global search strategy that allows for moving from one local minimizer to a better one. The efficiency of this strategy is illustrated by results of numerical experiments performed for some problems related to the design of filter networks.

    Download full text (pdf)
    TR2011-17
  • 26.
    Andersson, Mats
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Burdakov, Oleg
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Zikrin, Spartak
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Global Search Strategies for Solving Multilinear Least-squares Problems2011Report (Other academic)
    Abstract [en]

    The multilinear least-squares (MLLS) problem is an extension of the linear least-squares problem. The difference is that a multilinearoperator is used in place of a matrix-vector product. The MLLS istypically a large-scale problem characterized by a large number of local minimizers. It originates, for instance, from the design of filter networks. We present a global search strategy that allows formoving from one local minimizer to a better one. The efficiencyof this strategy isillustrated by results of numerical experiments performed forsome problems related to the design of filter networks.

    Download full text (pdf)
    Global Search Strategies for Solving Multilinear Least-squares Problems
  • 27.
    Andersson, Mats
    et al.
    Linköping University, Department of Biomedical Engineering. Linköping University, The Institute of Technology.
    Burdakov, Oleg
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Zikrin, Spartak
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Sparsity Optimization in Design of Multidimensional Filter Networks2013Report (Other academic)
    Abstract [en]

    Filter networks is a powerful tool used for reducing the image processing time, while maintaining its reasonably high quality.They are composed of sparse sub-filters whose low sparsity ensures fast image processing.The filter network design is related to solvinga sparse optimization problem where a cardinality constraint bounds above the sparsity level.In the case of sequentially connected sub-filters, which is the simplest network structure of those considered in this paper, a cardinality-constrained multilinear least-squares (MLLS) problem is to be solved. If to disregard the cardinality constraint, the MLLS is typically a large-scale problem characterized by a large number of local minimizers. Each of the local minimizers is singular and non-isolated.The cardinality constraint makes the problem even more difficult to solve.An approach for approximately solving the cardinality-constrained MLLS problem is presented.It is then applied to solving a bi-criteria optimization problem in which both thetime and quality of image processing are optimized. The developed approach is extended to designing filter networks of a more general structure. Its efficiency is demonstrated by designing certain 2D and 3D filter networks. It is also compared with the existing approaches.

    Download full text (pdf)
    Sparsity Optimization in Design of Multidimensional Filter Networks (revised version)
  • 28.
    Andersson, Mats
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Burdakov, Oleg
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Zikrin, Spartak
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Sparsity Optimization in Design of Multidimensional Filter Networks2015In: Optimization and Engineering, ISSN 1389-4420, E-ISSN 1573-2924, Vol. 16, no 2, p. 259-277Article in journal (Refereed)
    Abstract [en]

    Filter networks are used as a powerful tool used for reducing the image processing time and maintaining high image quality.They are composed of sparse sub-filters whose high sparsity ensures fast image processing.The filter network design is related to solvinga sparse optimization problem where a cardinality constraint bounds above the sparsity level.In the case of sequentially connected sub-filters, which is the simplest network structure of those considered in this paper, a cardinality-constrained multilinear least-squares (MLLS) problem is to be solved. Even when disregarding the cardinality constraint, the MLLS is typically a large-scale problem characterized by a large number of local minimizers, each of which is singular and non-isolated.The cardinality constraint makes the problem even more difficult to solve.

    An approach for approximately solving the cardinality-constrained MLLS problem is presented.It is then applied to solving a bi-criteria optimization problem in which both thetime and quality of image processing are optimized. The developed approach is extended to designing filter networks of a more general structure. Its efficiency is demonstrated by designing certain 2D and 3D filter networks. It is also compared with the existing approaches.

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    fulltext
  • 29.
    Andersson, Niclas
    Linköping University, Department of Computer and Information Science. Linköping University, The Institute of Technology.
    Compilation of mathematical models to parallel code1996Licentiate thesis, monograph (Other academic)
    Abstract [en]

    Generating parallel code from high-level mathematical models is in its general form an intractable problem. Rather than trying to solve this problem, a more realistic approach is to solve specific problem instances for limited domains.In this thesis, we focus our efforts on problems where the main computation is to solve ordinary differential equation systems. When solving such a system of equations, the major part of the computing time is spent in application specific code, rather than in the serial solver kernel. By applying domain specific knowledge, we can generate efficient parallel code for numerical solution.We investigate automatic parallelisation of the computation of ordinary differential equation systems at three different levels of granularity: equation system level, equation level, and clustered task level. At the clustered task level we employ existing scheduling and clustering algorithms to partition and distribute the computation.Moreover, an interface is provided to express explicit parallelism through annotations in the the mathematical model.This work is performed in the context of ObjectMath, a programming environment and modelling language that supports classes of equation objects, inheritance of equations, and solving systems of equations. The environment is designed to handle realistic problems.

  • 30. Order onlineBuy this publication >>
    Andersson, Per-Åke
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Multi-year maintenance optimisation for paved public roads - segment based modelling and price-directive decomposition2007Doctoral thesis, monograph (Other academic)
    Abstract [en]

    The thesis deals with the generation of cost efficient maintenance plans for paved roads, based on database information about the current surface conditions and functional models for costs and state changes, partly developed in cooperation with Vägverket (VV, Swedish Road Administration). The intended use is in a stage of budgeting and planning, before concrete project information is available. Unlike the up to now used models, individual maintenance plans can be formulated for each segment (a homogeneous road section as to the current pavement state and paving history), in continuous state and works spaces. By using Lagrangean relaxation optimisation techniques, the special benefit/cost-ratio constraints that VV puts on each maintenance project can be naturally mastered by dual prices for the budget constraints. The number of segments competing for budget resources is usually large. Data from VV Vägdatabank (SRA Road Database) in county Värmland were used, comprising around 9000 road segments. Due to the large data amount the implemented programs rely on parallel computation. During the thesis work, access to the PC-cluster Monolith at NSC was granted. In order to reduce optimisation run times, model & method development was needed. By aggregating the road segments into road classes, good initial values of the dual prices were achieved. By adding new state dimensions, the use of the Markov property could be motivated. By developing a special residual value routine, the explicitly considered time period could be reduced. At solving the dual subproblem special attention was paid to the discretization effects in the dynamic programming approach. One type of study is on a sub-network, e.g. a road. Validation studies were performed on road 63 in Värmland – with promising but not satisfactory results (see below). A special model for co-ordinated maintenance considers the fine-tuned cost effects of simultaneous maintenance of contiguous road segments. The other main type of study is for a whole network. Several method types have been applied, both for solving the relaxed optimisation problems and for generating maintenance plans that fit to the budgets. For a decent discretization, the run time for the whole Värmland network is less than 80 CPU-hrs.A posterior primal heuristics reduces the demands for parallel processing to a small PC-cluster.The thesis further studies the effects of redistributing budget means, as well as turning to a transparent stochastic model – both showing modest deviations from the basic model.

    Optimisation results for Värmland indicate budget levels around 40% of the actual Värmland budget as sufficient. However, important cost triggers are missing in this first model round, e.g., certain functional performance (safety), all environmental performance (noise etc.) and structural performance (e.g. bearing capacity, only modelled by an age measure). For increased credibility of PMS in general and optimisation in particular, the discrepancies should be further analysed and lead to improvements as to condition monitoring, state effect & cost modelling and mathematical modelling & implementation.

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  • 31.
    Anistratov, Pavel
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    Computation of Autonomous Safety Maneuvers Using Segmentation and Optimization2019Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis studies motion planning for future autonomous vehicles with main focus on passenger cars. By having automatic steering and braking together with information about the environment, such as other participants in the traffic or obstacles, it would be possible to perform autonomous maneuvers while taking limitations of the vehicle and road–tire interaction into account. Motion planning is performed to find such maneuvers that bring the vehicle from the current state to a desired future state, here by formulating the motion-planning problem as an optimal control problem. There are a number of challenges for such an approach to motion planning; some of them are how to formulate the criterion in the motion planning (objective function in the corresponding optimal control problem), and how to make the solution of motion-planning problems efficient to be useful in online applications. These challenges are addressed in this thesis.

    As a criterion for motion-planning problems of passenger vehicles on doublelane roads, it is investigated to use a lane-deviation penalty function to capture the observation that it is dangerous to drive in the opposing lane, but safe to drive in the original lane after the obstacle. The penalty function is augmented with certain additional terms to address also the recovery behavior of the vehicle. The resulting formulation is shown to provide efficient and steady maneuvers and gives a lower time in the opposing lane compared to other objective functions. Under varying parameters of the scenario formulation, the resulting maneuvers are changing in a way that exhibits structured characteristics.

    As an approach to improve efficiency of computations for the motion-planning problem, it is investigated to segment motion planning of the full maneuver into several smaller maneuvers. A way to extract segments is considered from a vehicle dynamics point of view, and it is based on extrema of the vehicle orientation and the yaw rate. The segmentation points determined using this approach are observed to allow efficient splitting of the optimal control problem for the full maneuver into subproblems.

    Having a method to segment maneuvers, this thesis further studies methods to allow parallel computation of these maneuvers. One investigated method is based on Lagrange relaxation and duality decomposition. Smaller subproblems are formulated, which are governed by solving a low-complexity coordination problem. Lagrangian relaxation is performed on a subset of the dynamic constraints at the segmentation points, while the remaining variables are predicted. The prediction is possible because of the observed structured characteristics resulting from the used lane-deviation penalty function. An alternative approach is based on adoption of the alternating augmented Lagrangian method. Augmentation of the Lagrangian allows to apply relaxation for all dynamic constraints at the segmentation points, and the alternating approach makes it possible to decompose the full problem into subproblems and coordinating their solutions by analytically solving an overall coordination problem. The presented decomposition methods allow computation of maneuvers with high correspondence and lower computational times compared to the results obtained for solving the full maneuver in one step.

    List of papers
    1. Segmentation and Merging of Autonomous At-the-Limit Maneuvers for Ground Vehicles
    Open this publication in new window or tab >>Segmentation and Merging of Autonomous At-the-Limit Maneuvers for Ground Vehicles
    2018 (English)In: Proceedings of the 14th International Symposium on Advanced Vehicle Control, Beijing, July 16-20, 2018, 2018, p. 1-6Conference paper, Published paper (Refereed)
    Abstract [en]

    To decrease the complexity of motion-planning optimizations, a segmentation and merging strategy for maneuvers is proposed. Maneuvers that are at-the-limit of friction are of special interest since they appear in many critical situations. The segmentation pointsare used to set constraints for several smaller optimizations for parts of the full maneuver, which later are merged and compared withoptimizations of the full maneuver. The technique is illustrated for a double lane-change maneuver.

    Keywords
    vehicle automation and control, ground vehicle motion-planning, aggressive maneuvers
    National Category
    Control Engineering
    Identifiers
    urn:nbn:se:liu:diva-152222 (URN)
    Conference
    The 14th International Symposium on Advanced Vehicle Control, Beijing, July 16-20, 2018
    Available from: 2018-10-22 Created: 2018-10-22 Last updated: 2021-05-26Bibliographically approved
    2. Efficient Motion Planning for Autonomous Vehicle Maneuvers Using Duality-Based Decomposition
    Open this publication in new window or tab >>Efficient Motion Planning for Autonomous Vehicle Maneuvers Using Duality-Based Decomposition
    2019 (English)In: IFAC PAPERSONLINE, ELSEVIER , 2019, Vol. 52, no 5, p. 78-84Conference paper, Published paper (Refereed)
    Abstract [en]

    A method to decompose a motion-planning problem into several segments is presented. It is based on a modification of the original problem, such that certain variables at the splitting points are considered to be precomputed and thus fixed and the remaining variables are obtained by performing Lagrange relaxation. The resulting dual problem is split into several subproblems, allowing parallel computation. The method is formalized as a computational algorithm and evaluated in a safety critical double lane-change situation. The resulting maneuver has close-to-optimal behavior and, for certain initialization strategies, it is obtained in shorter computational time compared to computing the full maneuver in one step. (C) 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

    Place, publisher, year, edition, pages
    ELSEVIER, 2019
    Series
    IFAC papers online, E-ISSN 2405-8963
    Keywords
    trajectory and path planning; autonomous vehicles; duality-based decomposition; motion control; safety; intelligent transportation systems
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:liu:diva-161215 (URN)10.1016/j.ifacol.2019.09.013 (DOI)000486629500014 ()
    Conference
    9th IFAC International Symposium on Advances in Automotive Control (AAC)
    Note

    Funding Agencies|Wallenberg AI, Autonomous Systems and Software Program (WASP) - Knut and Alice Wallenberg Foundation

    Available from: 2019-10-25 Created: 2019-10-25 Last updated: 2021-08-23
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    Computation of Autonomous Safety Maneuvers Using Segmentation and Optimization
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  • 32.
    Anistratov, Pavel
    et al.
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    Olofsson, Björn
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    Burdakov, Oleg
    Linköping University, Department of Mathematics, Optimization. Linköping University, Faculty of Science & Engineering.
    Nielsen, Lars
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    Autonomous-Vehicle Maneuver Planning Using Segmentation and the Alternating Augmented Lagrangian Method2020In: 21th IFAC World Congress Proceedings / [ed] Rolf Findeisen, Sandra Hirche, Klaus Janschek, Martin Mönnigmann, Elsevier, 2020, Vol. 53, p. 15558-15565Conference paper (Refereed)
    Abstract [en]

    Segmenting a motion-planning problem into smaller subproblems could be beneficial in terms of computational complexity. This observation is used as a basis for a new sub-maneuver decomposition approach investigated in this paper in the context of optimal evasive maneuvers for autonomous ground vehicles. The recently published alternating augmented Lagrangianmethod is adopted and leveraged on, which turns out to fit the problem formulation with several attractive properties of the solution procedure. The decomposition is based on moving the coupling constraints between the sub-maneuvers into a separate coordination problem, which is possible to solve analytically. The remaining constraints and the objective function are decomposed into subproblems, one for each segment, which means that parallel computation is possible and benecial. The method is implemented and evaluated in a safety-critical double lane-change scenario. By using the solution of a low-complexity initialization problem and applying warm-start techniques in the optimization, a solution is possible to obtain after just a few alternating iterations using the developed approach. The resulting computational time is lower than solving one optimization problem for the full maneuver.

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  • 33.
    Anistratov, Pavel
    et al.
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    Olofsson, Björn
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering. Lund Univ, Sweden.
    Nielsen, Lars
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    Efficient Motion Planning for Autonomous Vehicle Maneuvers Using Duality-Based Decomposition2019In: IFAC PAPERSONLINE, ELSEVIER , 2019, Vol. 52, no 5, p. 78-84Conference paper (Refereed)
    Abstract [en]

    A method to decompose a motion-planning problem into several segments is presented. It is based on a modification of the original problem, such that certain variables at the splitting points are considered to be precomputed and thus fixed and the remaining variables are obtained by performing Lagrange relaxation. The resulting dual problem is split into several subproblems, allowing parallel computation. The method is formalized as a computational algorithm and evaluated in a safety critical double lane-change situation. The resulting maneuver has close-to-optimal behavior and, for certain initialization strategies, it is obtained in shorter computational time compared to computing the full maneuver in one step. (C) 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

  • 34.
    Arctaedius, Gunnar
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    A Novel Method for Finding Overlap Depth: Development of ArtiaX, a ChimeraX plugin2023Independent thesis Advanced level (degree of Master (Two Years)), 28 HE creditsStudent thesis
    Abstract [en]

    Visualization and image filtering are important parts of cryo-electron tomography analysis. ArtiaX, a plugin developed for UCSF ChimeraX, has been extended to improve the functionality of these two parts. For the visualization, a method of moving 3D surfaces to remove overlap between them has been developed and implemented. To accommodate this, a Monte Carlo approach using Poisson disc sampling for approximating volume of overlap between 3D surfaces is used, and a novel method for measuring overlap has been invented, called the Normal Projection Method, useful for measuring the depth of overlap between surfaces. For the image filtering, tomogram averaging and frequency filters have been added to the ArtiaX toolbox.

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    A Novel Method for Finding Overlap Depth: Development of ArtiaX, a ChimeraX plugin
  • 35.
    Arndt, Carl-Fredrik
    Linköping University, Department of Mathematics, Scientific Computing.
    Energy estimates and variance estimation for hyperbolic stochastic partial differentialequations2011Independent thesis Advanced level (professional degree), 30 credits / 45 HE creditsStudent thesis
    Abstract [en]

    In this thesis the connections between the boundary conditions and the vari- ance of the solution to a stochastic partial differential equation (PDE) are investigated. In particular a hyperbolical system of PDE’s with stochastic initial and boundary data are considered. The problem is shown to be well- posed on a class of boundary conditions through the energy method. Stability is shown by using summation-by-part operators coupled with simultaneous- approximation-terms. By using the energy estimates, the relative variance of the solutions for different boundary conditions are analyzed. It is concluded that some types of boundary conditions yields a lower variance than others. This is verified by numerical computations.

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  • 36.
    Arnlind, Joakim
    et al.
    Department of Mathematics, Royal Institute of Technology, 100 44, Stockholm, Sweden .
    Bordemann, Martin
    Laboratoire de MIA, 4 rue des Frères Lumière, Univ. deHaute-Alsace, 68093, Mulhouse, France .
    Hoppe, Jens
    Department of Mathematics, Royal Institute of Technology, 100 44, Stockholm, Sweden .
    Lee, Choonkyu
    Department of Physics and Center for Theoretical Physics, Seoul National University, 151-747, Seoul, South Korea .
    Goldfish Geodesics and Hamiltonian Reduction of Matrix Dynamics2008In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 84, p. 89-98Article in journal (Refereed)
    Abstract [en]

    We describe the Hamiltonian reduction of a time-dependent real-symmetric N×N matrix system to free vector dynamics, and also provide a geodesic interpretation of Ruijsenaars–Schneider systems. The simplest of the latter, the goldfish equation, is found to represent a flat-space geodesic in curvilinear coordinates.

  • 37.
    Arnlind, Joakim
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Choe, Jaigyoung
    Korea Institute Adv Study, South Korea.
    Hoppe, Jens
    Royal Institute Technology, Sweden.
    Noncommutative Minimal Surfaces2016In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 106, no 8, p. 1109-1129Article in journal (Refereed)
    Abstract [en]

    We define noncommutative minimal surfaces in the Weyl algebra, and give a method to construct them by generalizing the well-known Weierstrass representation.

  • 38.
    Arnlind, Joakim
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Holm, Christoffer
    Linköping University, Department of Mathematics. Linköping University, Faculty of Science & Engineering.
    A noncommutative catenoid2018In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 108, no 7, p. 1601-1622Article in journal (Refereed)
    Abstract [en]

    A noncommutative algebra corresponding to the classical catenoid is introduced together with a differential calculus of derivations. We prove that there exists a unique metric and torsion-free connection that is compatible with the complex structure, and the curvature is explicitly calculated. A noncommutative analogue of the fact that the catenoid is a minimal surface is studied by constructing a Laplace operator from the connection and showing that the embedding coordinates are harmonic. Furthermore, an integral is defined and the total curvature is computed. Finally, classes of left and right modules are introduced together with constant curvature connections, and bimodule compatibility conditions are discussed in detail.

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  • 39.
    Arnlind, Joakim
    et al.
    Department of Mathematics, Royal Institute of Technology, Stockholm, 100 44, Sweden .
    Hoppe, Jens
    Department of Mathematics, Royal Institute of Technology, Stockholm, 100 44, Sweden .
    EIGENVALUE DYNAMICS, FOLLYTONS AND LARGEN LIMITS OF MATRICES2006In: Applications of Random Matrices in Physics / [ed] Édouard Brézin, Vladimir Kazakov, Didina Serban, Paul Wiegmann, Anton Zabrodin, Springer, 2006, 211, p. 89-94Chapter in book (Refereed)
    Abstract [en]

    How do the eigenvalues of a “free” hermitian N × N matrix X(t) evolve in time? The answer is provided by the rational Calogero-Moser systems [5, 13] if (!) the initial conditions are chosen such that i[X(0),Ẋ(0)] has a non-zero eigenvalue of multiplicity N–1; for generic X(0),Ẋ(0) the question remained unanswered for 30 years.

  • 40.
    Arnlind, Joakim
    et al.
    Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden.
    Hoppe, Jens
    Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden.
    Eigenvalue-Dynamics off the Calogero–Moser System2004In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 68, p. 121-129Article in journal (Refereed)
    Abstract [en]

    By finding N(N− 1)/2 suitable conserved quantities, free motions of real symmetric N×N matrices X(t), with arbitrary initial conditions, are reduced to nonlinear equations involving only the eigenvalues of X – in contrast to the rational Calogero-Moser system, for which [X(0),Xd(0)] has to be purely imaginary, of rank one.

  • 41.
    Arnlind, Joakim
    et al.
    Department of Mathematics, Royal Institute of Technology, 10044 Stockholm, Sweden.
    Hoppe, Jens
    Department of Mathematics, Royal Institute of Technology, 10044 Stockholm, Sweden.
    Theisen, Stefan
    Albert-Einstein-Institut, Am Mühlenberg 1, D-14476 Golm, Germany.
    Spinning membranes2004In: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 599, no 1-2, p. 118-128Article in journal (Refereed)
    Abstract [en]

    We present new solutions of the classical equations of motion of bosonic (matrix-)membranes. Those relating to minimal surfaces in spheres provide spinning membrane solutions in AdSp×SqAdSp×Sq, as well as in flat space–time. Nontrivial reductions of the BMN matrix model equations are also given.

  • 42.
    Arnlind, Joakim
    et al.
    Mathematical Physics, Royal Institute of Technology, SE-106 91, Stockholm, Sweden .
    Mickelsson, Jouko
    Mathematical Physics, Royal Institute of Technology, SE-106 91, Stockholm, Sweden .
    Trace Extensions, Determinant Bundles, and Gauge Group Cocycles2002In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 62, no 2, p. 101-110Article in journal (Refereed)
    Abstract [en]

    We study the geometry of determinant line bundles associated with Dirac operators on compact odd-dimensional manifolds. Physically, these arise as (local) vacuum line bundles in quantum gauge theory. We give a simplified derivation of the commutator anomaly formula using a construction based on noncyclic trace extensions and associated nonmultiplicative renormalized determinants.

  • 43.
    Arnström, Daniel
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Bemporad, Alberto
    IMT Sch Adv Studies Lucca, Italy.
    Axehill, Daniel
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    A Dual Active-Set Solver for Embedded Quadratic Programming Using Recursive LDLT Updates2022In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 67, no 8, p. 4362-4369Article in journal (Refereed)
    Abstract [en]

    In this technical article, we present a dual active-set solver for quadratic programming that has properties suitable for use in embedded model predictive control applications. In particular, the solver is efficient, can easily be warm started, and is simple to code. Moreover, the exact worst-case computational complexity of the solver can be determined offline and, by using outer proximal-point iterations, ill-conditioned problems can be handled in a robust manner.

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  • 44.
    Arnström, Daniel
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Bemporad, Alberto
    IMT Sch Adv Studies Lucca, Italy.
    Axehill, Daniel
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    A Linear Programming Method Based on Proximal-Point Iterations With Applications to Multi-Parametric Programming2022In: IEEE Control Systems Letters, E-ISSN 2475-1456, Vol. 6, p. 2066-2071Article in journal (Refereed)
    Abstract [en]

    We propose a linear programming method that is based on active-set changes and proximal-point iterations. The method solves a sequence of least-distance problems using a warm-started quadratic programming solver that can reuse internal matrix factorizations from the previously solved least-distance problem. We show that the proposed method terminates in a finite number of iterations and that it outperforms state-of-the-art LP solvers in scenarios where an extensive number of small/medium scale LPs need to be solved rapidly, occurring in, for example, multi-parametric programming algorithms. In particular, we show how the proposed method can accelerate operations such as redundancy removal, computation of Chebyshev centers and solving linear feasibility problems.

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  • 45.
    Arnström, Daniel
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Bemporad, Alberto
    IMT Sch Adv Studies Lucca, Italy.
    Axehill, Daniel
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Complexity Certification of Proximal-Point Methods for Numerically Stable Quadratic Programming2021In: 2021 AMERICAN CONTROL CONFERENCE (ACC), IEEE , 2021, p. 947-952Conference paper (Refereed)
    Abstract [en]

    When solving a quadratic program (QP), one can improve the numerical stability of any QP solver by performing proximal-point outer iterations, resulting in solving a sequence of better conditioned QPs. In this paper we present a method which, for a given multi-parametric quadratic program (mpQP) and any polyhedral set of parameters, determines which sequences of QPs will have to be solved when using outer proximal-point iterations. By knowing this sequence, bounds on the worst-case complexity of the method can be obtained, which is of importance in, for example, real-time model predictive control (MPC) applications. Moreover, we combine the proposed method with previous work on complexity certification for active-set methods to obtain a more detailed certification of the proximal-point methods complexity, namely the total number of inner iterations.

  • 46.
    Arnström, Daniel
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Bemporad, Alberto
    IMT Sch Adv Studies Lucca, Italy.
    Axehill, Daniel
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Complexity Certification of Proximal-Point Methods for Numerically Stable Quadratic Programming2021In: IEEE Control Systems Letters, E-ISSN 2475-1456, Vol. 5, no 4, p. 1381-1386Article in journal (Refereed)
    Abstract [en]

    When solving a quadratic program (QP), one can improve the numerical stability of any QP solver by performing proximal-point outer iterations, resulting in solving a sequence of better conditioned QPs. In this letter we present a method which, for a given multi-parametric quadratic program (mpQP) and any polyhedral set of parameters, determines which sequences of QPs will have to be solved when using outer proximal-point iterations. By knowing this sequence, bounds on the worst-case complexity of the method can be obtained, which is of importance in, for example, real-time model predictive control (MPC) applications. Moreover, we combine the proposed method with previous work on complexity certification for active-set methods to obtain a more detailed certification of the proximal-point methods complexity, namely the total number of inner iterations.

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  • 47.
    Aronsson, Gunnar
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    On Production Planning and Activity Periods2015Report (Other academic)
    Abstract [en]

    Consider a company which produces and sells a certain product on a market with highly variable demand. Since the demand is very high during some periods, the company will produce and create a stock in advance before these periods. On the other hand it costs money to hold a big stock, so that some balance is needed for optimum. The demand is assumed to be known in advance with sufficient accuracy. We use a technique from optimal control theory for the analysis, which leads to so-called activity periods. During such a period the stock is positive and the production is maximal, provided that the problem starts with zero stock, which is the usual case. Over a period of one or more years, there will be a few activity periods. Outside these periods the stock is zero and the policy is to choose production = the smaller of [demand, maximal production]. The “intrinsic time length” is a central concept. It is simply the maximal time a unit of the product can be stored before selling without creating a loss.

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    On Production Planning and Activity Periods
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  • 48.
    Aronsson, Gunnar
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Production planning, activity periods and passivity periods2015Report (Other academic)
    Abstract [en]

    Consider a company which produces and sells a certain product on a market with highly variable demand. Since the demand is very high during some periods, the company will produce and create a stock in advance before these periods. On the other hand it costs money to hold a big stock, so that some balance is needed for optimum. The demand is assumed to be known in advance with sufficient accuracy. We use a technique from optimal control theory for the analysis, which leads to so-called activity periods. During such a period the stock is positive and the production is maximal, provided that the problem starts with zero stock, which is the usual case. Over a period of one or more years, there will be a few activity periods. Outside these periods the stock is zero and the policy is to choose production = the smaller of [demand, maximal production]. The “intrinsic time length” is a central concept. It is simply the maximal time a unit of the product can be stored before selling without creating a loss.

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  • 49.
    Arop, Martin Deosborns
    et al.
    Makerere Univ, Uganda; Muni Univ, Uganda.
    Kasumba, Henry
    Makerere Univ, Uganda.
    Kasozi, Juma
    Makerere Univ, Uganda.
    Berntsson, Fredrik
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Optimal Actuator Placement for Control of Vibrations Induced by Pedestrian-Bridge Interactions2023In: MATHEMATICS IN APPLIED SCIENCES AND ENGINEERING, ISSN 2563-1926, Vol. 4, no 3, p. 172-195Article in journal (Refereed)
    Abstract [en]

    In this paper, an optimal actuator placement problem with a linear wave equation as the constraint is considered. In particular, this work presents the frameworks for finding the best location of actuators depending upon the given initial conditions, and where the dependence on the initial conditions is averaged out. The problem is motivated by the need to control vibrations induced by pedestrian-bridge interactions. An approach based on shape optimization techniques is used to solve the problem. Specifically, the shape sensitivities involving a cost functional are determined using the averaged adjoint approach. A numerical algorithm based on these sensitivities is used as a solution strategy. Numerical results are consistent with the theoretical results, in the two examples considered.

  • 50.
    Baravdish, George
    et al.
    Linköping University, Department of Science and Technology, Physics, Electronics and Mathematics. Linköping University, Faculty of Science & Engineering.
    Johansson, Tomas
    Linköping University, Department of Science and Technology, Physics, Electronics and Mathematics. Linköping University, Faculty of Science & Engineering.
    Svensson, Olof
    Linköping University, Department of Science and Technology, Physics, Electronics and Mathematics. Linköping University, Faculty of Science & Engineering.
    Ssebunjo, W.
    Makarere Univ, Uganda.
    Identifying a response parameter in a model of brain tumour evolution under therapy2023In: IMA Journal of Applied Mathematics, ISSN 0272-4960, E-ISSN 1464-3634, Vol. 88, no 2, p. 378-404Article in journal (Refereed)
    Abstract [en]

    A nonlinear conjugate gradient method is derived for the inverse problem of identifying a treatment parameter in a nonlinear model of reaction-diffusion type corresponding to the evolution of brain tumours under therapy. The treatment parameter is reconstructed from additional information about the tumour taken at a fixed instance of time. Well-posedness of the direct problems used in the iterative method is outlined as well as uniqueness of a solution to the inverse problem. Moreover, the parameter identification is recasted as the minimization of a Tikhonov type functional and the existence of a minimizer to this functional is shown. Finite-difference discretization of the space and time derivatives are employed for the numerical implementation. Numerical simulations on full 3D brain data are included showing that information about a spacewise-dependent treatment parameter can be recovered in a stable way.

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