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Distributed primal-€dual interior-point methods for solving tree-structured coupled convex problems using message-passing
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
Department of Applied Mathematics and Computer Science, Technical University of Denmark, Lyngby, Denmark.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
2016 (English)In: Optimization Methods and Software, ISSN 1055-6788, E-ISSN 1029-4937, 1-35 p.Article in journal (Refereed) Epub ahead of print
Abstract [en]

In this paper, we propose a distributed algorithm for solving coupled problems with chordal sparsity or an inherent tree structure which relies on primal–dual interior-point methods. We achieve this by distributing the computations at each iteration, using message-passing. In comparison to existing distributed algorithms for solving such problems, this algorithm requires far fewer iterations to converge to a solution with high accuracy. Furthermore, it is possible to compute an upper-bound for the number of required iterations which, unlike existing methods, only depends on the coupling structure in the problem. We illustrate the performance of our proposed method using a set of numerical examples.

Place, publisher, year, edition, pages
Taylor & Francis, 2016. 1-35 p.
National Category
Control Engineering Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-133995DOI: 10.1080/10556788.2016.1213839OAI: oai:DiVA.org:liu-133995DiVA: diva2:1066110
Note

The previous status of this article was Manuscript and the working title was Distributed Primal-dual Interior-point Methods for Solving Loosely Coupled Problems Using Message Passing.

Available from: 2017-01-17 Created: 2017-01-17 Last updated: 2017-01-17Bibliographically approved
In thesis
1. Divide and Conquer: Distributed Optimization and Robustness Analysis
Open this publication in new window or tab >>Divide and Conquer: Distributed Optimization and Robustness Analysis
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

As control of large-scale complex systems has become more and more prevalent within control, so has the need for analyzing such controlled systems. This is particularly due to the fact that many of the control design approaches tend to neglect intricacies in such systems, e.g., uncertainties, time delays, nonlinearities, so as to simplify the design procedure.

Robustness analysis techniques allow us to assess the effect of such neglected intricacies on performance and stability. Performing robustness analysis commonly requires solving an optimization problem. However, the number of variables of this optimization problem, and hence the computational time, scales badly with the dimension of the system. This limits our ability to analyze large-scale complex systems in a centralized manner. In addition, certain structural constraints, such as privacy requirements or geographical separation, can prevent us from even forming the analysis problem in a centralized manner.

In this thesis, we address these issues by exploiting structures that are common in large-scale systems and/or their corresponding analysis problems. This enables us to reduce the computational cost of solving these problems both in a centralized and distributed manner. In order to facilitate distributed solutions, we employ or design tailored distributed optimization techniques. Particularly, we propose three distributed optimization algorithms for solving the analysis problem, which provide superior convergence and/or computational properties over existing algorithms. Furthermore, these algorithms can also be used for solving general loosely coupled optimization problems that appear in a variety of fields ranging from control, estimation and communication systems to supply chain management and economics.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2015. 330 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1676
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-117503 (URN)10.3384/diss.diva-117503 (DOI)978-91-7519-050-1 (ISBN)
Public defence
2015-06-11, Visionen, Hus B, Campus Valla, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2015-05-04 Created: 2015-04-29 Last updated: 2017-01-17Bibliographically approved

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