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  • 1.
    Björk, Kaj-Mikael
    et al.
    Process Design Laboratory, Åbo Akademi University, Åbo, Finland.
    Lindberg, Per Olov
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Westerlund, Tapio
    Process Design Laboratory, Åbo Akademi University, Åbo, Finland.
    Some convexifications in global optimization of problems containing signomial terms2003In: Computers and Chemical Engineering, ISSN 0098-1354, E-ISSN 1873-4375, Vol. 27, no 5, p. 669-679Article in journal (Refereed)
    Abstract [en]

    It is often possible to use different convexification techniques with different transformations in global optimization. In 'Optimization Eng. (submitted for publication)', a new global optimization technique based on convexifying signomial terms is presented. The technique is based on the solution of a sequence of convexified approximate subproblems. The choice of transformation functions is clearly essential. It is not enough to use convexifications that will result in convex and underestimating problems, if an effective optimization approach is wanted. The transformations should be such that they make the resulting problems convex but at the same time do not change the problem more than necessary. It will be shown in this article that for certain problems the choice of transformations has a clear influence on the efficiency of the proposed optimization approach. Using other transformations than what is proposed in 'Optimization Eng. (submitted for publication)' will, in some examples, give solution times that are shorter by an order of magnitude. The concept of power convex functions (Generalized Concavity Optimization Econ. (1981) 153) will be used as a measure of the quality of the transformations. In this paper, the new transformation functions are also shown to be very successful in a heat exchanger network synthesis application. © 2002 Elsevier Science Ltd. All rights reserved.

  • 2.
    Blomvall, Jörgen
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Lindberg, Per Olov
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    A Riccati-based primal interior point solver for multistage stochastic programming2002In: European Journal of Operational Research, ISSN 0377-2217, E-ISSN 1872-6860, Vol. 143, no 2, p. 452-461Article in journal (Refereed)
    Abstract [en]

    We propose a new method for certain multistage stochastic programs with linear or nonlinear objective function, combining a primal interior point approach with a linear-quadratic control problem over the scenario tree. The latter problem, which is the direction finding problem for the barrier subproblem is solved through dynamic programming using Riccati equations. In this way we combine the low iteration count of interior point methods with an efficient solver for the subproblems. The computational results are promising. We have solved a financial problem with 1,000,000 scenarios, 15,777,740 variables and 16,888,850 constraints in 20 hours on a moderate computer. © 2002 Elsevier Science B.V. All rights reserved.

  • 3.
    Blomvall, Jörgen
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Lindberg, Per Olov
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    A Riccati-based primal interior point solver for multistage stochastic programming - Extensions2002In: Optimization Methods and Software, ISSN 1055-6788, E-ISSN 1029-4937, Vol. 17, no 3, p. 383-407Article in journal (Refereed)
    Abstract [en]

    We show that a Riccati-based Multistage Stochastic Programming solver for problems with separable convex linear/nonlinear objective developed in previous papers can be extended to solve more general Stochastic Programming problems. With a Lagrangean relaxation approach, also local and global equality constraints can be handled by the Riccati-based primal interior point solver. The efficiency of the approach is demonstrated on a 10 staged stochastic programming problem containing both local and global equality constraints. The problem has 1.9 million scenarios, 67 million variables and 119 million constraints, and was solved in 97 min on a 32 node PC cluster.

  • 4.
    Blomvall, Jörgen
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Lindberg, Per Olov
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Back-testing the performance of an actively managed option portfolio at the Swedish Stock Market, 1990–19992003In: Journal of Economic Dynamics and Control, ISSN 0165-1889, E-ISSN 1879-1743, Vol. 27, no 6, p. 1099-1112Article in journal (Refereed)
    Abstract [en]

    We build an investment model based on Stochastic Programming. In the model we buy at the ask price and sell at the bid price. We apply the model to a case where we can invest in a Swedish stock index, call options on the index and the risk-free asset. By reoptimizing the portfolio on a daily basis over a ten-year period, it is shown that options can be used to create a portfolio that outperforms the index. With ex post analysis, it is furthermore shown that we can create a portfolio that dominates the index in terms of mean and variance, i.e. at given level of risk we could have achieved a higher return using options.

  • 5.
    Daneva, Maria
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Lindberg, Per Olov
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    A Conjugate Direction Frank-Wolfe Method for Nonconvex Problems2003Report (Refereed)
    Abstract [en]

    In this paper we propose an algorithm for solving problems with nonconvex objective function and linear constraints. We extend the previously suggested Conjugate direction Frank–Wolfe algorithm to nonconvex problems. We apply our method to multi-class user equilibria under social marginal cost pricing. Results of numerical experiments on Sioux Falls and Winnipeg are reported.

  • 6.
    Daneva, Maria
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Lindberg, Per Olov
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    A Conjugate Direction Frank-Wolfe Method with Applications to the Traffic Assignment Problem2003In: Operations Research Proceedings 2002: Selected Papers of the International Conference on Operations Research (SOR 2002), Klagenfurt, September 2-5, 2002" / [ed] Leopold-Wildburger, U, Springer , 2003, p. -550Chapter in book (Other academic)
    Abstract [en]

    This proceedings volume contains a selection of papers presented at the International Conference on Operations Research (SOR 2002).The contributions cover the broad interdisciplinary spectrum of Operations Research and present recent advances in theory, development of methods, and applications in practice. Subjects covered are Production, Logistics and Supply Chain Production, Marketing and Data Analysis, Transportation and Traffic, Scheduling and Project Management, Telecommunication and Information Technology, Energy and Environment, Public Economy, Health, Agriculture, Education, Banking, Finance, Insurance, Risk Management, Continuous Optimization, Discrete and Combinatorial Optimization, Stochastic and Dynamic Programming, Simulation, Control Theory, Systems Dynamics, Dynamic Games, Game Theory, Auctioning and Bidding, Experimental Economics, Econometrics, Statistics and Mathematical Economics, Fuzzy Logic, Multicriteria Decision Making, Decision Theory.

  • 7.
    Daneva, Maria
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Lindberg, Per Olov
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Conjugate Direction Frank-Wolfe Methods with Applications to Traffic Assignment Problem2003In: International Symposium on Mathematical Programming,2003, 2003Conference paper (Other academic)
  • 8.
    Daneva (Mitradjieva), Maria
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Lindberg, Per Olov
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    The Stiff is Moving - Conjugate Direction Frank -Wolfe Methods with Applications to Traffic Assignment2013In: Transportation Science, ISSN 0041-1655, E-ISSN 1526-5447, Vol. 47, no 2, p. 280-293Article in journal (Refereed)
    Abstract [en]

    We present versions of the Frank-Wolfe method for linearly constrained convex programs, in which consecutive search directions are made conjugate. Preliminary computational studies in a MATLAB environment applying pure Frank-Wolfe, conjugate direction Frank-Wolfe (CFW), bi-conjugate Frank-Wolfe (BFW), and "partanized" Frank-Wolfe methods to some classical Traffic Assignment Problems show that CFW and BFW compare favorably to the other methods. This spurred a more detailed study, comparing our methods to an origin-based algorithm. This study indicates that our methods are competitive for accuracy requirements ensuring link flow stability. We also show that CFW is globally convergent. We further point at independent studies by other researchers that show that our methods compare favorably with recent bush-based and gradient projection algorithms on computers with several cores

  • 9.
    Engelson, Leonid
    et al.
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Lindberg, Per Olov
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Daneva, Maria
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Multi-Class User Equilibria under Social Marginal Cost Pricing2002In: Operations Research 2002, 2002, p. 174-179Conference paper (Other academic)
    Abstract [en]

    In the congested cities of today, congestion pricing is a tempting alternative. With a single user class, already Beckmann et al. showed that ``system optimal'' traffic flows can be achieved by social marginal cost (SMC) pricing where users have to pay for the delays the incur on others. However different user classes can have widly differing time values. Hence, when introducing tolls, one should consider multi-class user equilibria, where the classes have different time values. In the single class case, the equilibrium conditions can be viewn as optimality conditions of an equivalent optimization problem. In the multi-class case, however, netter claims that this is not possible. We show that, depending on the formulation, the multi-class SMC-pricing equilibrium problem (with different time values) can be stated either as an asymmetric or as a symmetric equilibrium problem. In the latter case, the corresponding optimization problems is in general non-convex. For this non-convex problem, we devise descent methods of Frank-Wolfe type. We apply the methods and study a synthetic case based on Sioux Falls.

  • 10.
    Golbaharan, Nima
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Lindberg, Per Olov
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Göthe-Lundgren, Maud
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Optimal Routing of Snowplows - A Column generation Approach2003In: Operations Research 2002,2002, Heidelberg: Springer , 2003, p. 199-Conference paper (Refereed)
  • 11.
    Hägglöf, Kristoffer
    et al.
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Lindberg, Per Olov
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    A dual algorithm for the convex multicommodity flow problemManuscript (preprint) (Other academic)
    Abstract [en]

    This paper introduces a new dual ascent algorithm for solving the convex multicommodity flow problem, CMFP for short. CMFPs arize in many different routing problems such as the design of packet switched computer networks and the computation of traffic network equilibria. The algorithm utilizes the structure of the dual convex multicommodity flow problem, DCMFP for short. The dual objective is a sum of a concave differentiable function and a piecewise linear concave function. The algorithm exploits the local structure of the dual objective in an ascent scheme. In this paper a thorough explanation of the CMFPs and DCMFPs are given along with an outline of the dual ascent algorithm proposed. The method are applied to CMFPs arizing in the traffic assignment setting.

  • 12.
    Hägglöf, Kristoffer
    et al.
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Lindgren, Per Olov
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    A comment on some test networks for the traffic assignment problemManuscript (preprint) (Other academic)
    Abstract [en]

    We show that many published test problems for traffic assignment algorithms have peculiarities. First and foremost, several of them have incorrectly specified attributes, such as the number of nodes. In other test-problems, the network contains subnetworks with constant travel times; subnetworks which to a large extent can be reduced or eliminated. In further test problems, the constant travel time subnetworks imply that the solution has nonunique arc flows.

  • 13.
    Kiwiel, Krzysztof C.
    et al.
    Systems Research Institute, Warszawa.
    Larsson, Torbjörn
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Lindberg, Per Olov
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Lagrangian relaxation via ballstep subgradient methods2007In: Mathematics of Operations Research, ISSN 0364-765X, E-ISSN 1526-5471, Vol. 32, no 3, p. 669-686Article in journal (Refereed)
    Abstract [en]

    We exhibit useful properties of ballstep subgradient methods for convex optimization using level controls for estimating the optimal value. Augmented with simple averaging schemes, they asymptotically find objective and constraint subgradients involved in optimality conditions. When applied to Lagrangian relaxation of convex programs, they find both primal and dual solutions, and have practicable stopping criteria. Up until now, similar results have only been known for proximal bundle methods, and for subgradient methods with divergent series stepsizes, whose convergence can be slow. Encouraging numerical results are presented for large-scale nonlinear multicommodity network flow problems. ©2007 INFORMS.

  • 14.
    Kiwiel, Krzysztof C
    et al.
    Systems Research Institute, Newelska.
    Olov Lindberg, Per
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Nou, Andreas
    Royal Institute of Technology, Stockholm.
    Bregman proximal relaxation of large-scale 0-1 problems2000In: Computational optimization and applications, ISSN 0926-6003, E-ISSN 1573-2894, Vol. 15, no 1, p. 33-44Article in journal (Refereed)
    Abstract [en]

    We apply a recent extension of the Bregman proximal method for convex programming to LP relaxations of 0-1 problems. We allow inexact subproblem solutions obtained via dual ascent, increasing their accuracy successively to retain global convergence. Our framework is applied to relaxations of large-scale set covering problems that arise in airline crew scheduling. Approximate relaxed solutions are used to construct primal feasible solutions via a randomized heuristic. Encouraging preliminary experience is reported.

  • 15.
    Lindberg, Per Olov
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Engelson, L.
    Convexification of the Traffic Equilibrium Problem with Social Marginal Cost Tolls2004In: Operations Research 2003,2003, Heidelberg: Springer , 2004, p. 141-Conference paper (Refereed)
  • 16.
    Lindberg, Per Olov
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Engelson, L.
    Samhällsekonomiskt optimala biltullar för trafikanter med olika tidsvärden,2003In: Transportforum,2003, 2003Conference paper (Other academic)
  • 17.
    Lindberg, Per Olov
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Eriksson, EA
    Mattsson, LG
    Linkoping Univ, Dept Math, S-58183 Linkoping, Sweden Natl Def Res Estab, Div Def Anal, S-17290 Stockholm, Sweden Royal Inst Technol, Dept Infrastruct & Planning, S-10044 Stockholm, Sweden.
    Homothetic functions revisited2002In: Economic Theory, ISSN 0938-2259, E-ISSN 1432-0479, Vol. 19, no 2, p. 417-427Article in journal (Refereed)
    Abstract [en]

    This paper examines the proposition that homotheticity is equivalent to the property that (e.g., in the context of a production function) the marginal rate of substitution is constant along any ray from the origin. This claim is made in many places, but hitherto the prerequisites have not been stated explicitly. In the present contribution it is demonstrated that an additional condition is required for the claim to hold. We present a theorem that achieves equivalence by also assuming 'nowhere ray constancy'. It turns out that this condition is implied by assumptions often made, e.g., in production theory. Further, a complete characterization is given of the class of functions that satisfy ray constant marginal rates of substitution or, somewhat more generally, a condition of ray parallel gradients. In addition to homothetic functions this class contains functions homogeneous of degree 0 (i.e., ray constant) and functions which are homothetic in disjoint regions separated by regions of ray constancy.

  • 18.
    Lindberg, Per Olov
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Golbaharan, Nima
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    A Prize Collecting Connected Subgraph Problem2003In: 18th Int. Symp. on Math. Programming,2003, 2003Conference paper (Other academic)
  • 19.
    Razmara, Gholamreza
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Lindberg, Per Olov
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    The Prize Collecting Connected Subgraph Problem - A New NP-Hard Problem arizing in Snow Removal Routing2004In: Operations Research 2004,2004, Berlin: Springer , 2004Conference paper (Refereed)
1 - 19 of 19
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