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Distributed solutions for loosely coupled feasibility problems using proximal splitting methods
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Technical University of Denmark, Kongens Lyngby, Denmark.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
2015 (English)In: Optimization Methods and Software, ISSN 1055-6788, Vol. 30, no 1, 128-161 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, we consider convex feasibility problems (CFPs) where the underlying sets are loosely coupled, and we propose several algorithms to solve such problems in a distributed manner. These algorithms are obtained by applying proximal splitting methods to convex minimization reformulations of CFPs. We also put forth distributed convergence tests which enable us to establish feasibility or infeasibility of the problem distributedly, and we provide convergence rate results. Under the assumption that the problem is feasible and boundedly linearly regular, these convergence results are given in terms of the distance of the iterates to the feasible set, which are similar to those of classical projection methods. In case the feasibility problem is infeasible, we provide convergence rate results that concern the convergence of certain error bounds.

Place, publisher, year, edition, pages
Taylor & Francis, 2015. Vol. 30, no 1, 128-161 p.
Keyword [en]
feasible/infeasible convex feasibility problems, proximal splitting, distributed solution, flow feasibility problem
National Category
Control Engineering
URN: urn:nbn:se:liu:diva-110124DOI: 10.1080/10556788.2014.902056ISI: 000345371800006OAI: diva2:742963
Available from: 2014-09-03 Created: 2014-09-03 Last updated: 2015-05-04
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.
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1676
National Category
Control Engineering
urn:nbn:se:liu:diva-117503 (URN)10.3384/diss.diva-117503 (DOI)978-91-7519-050-1 (print) (ISBN)
Public defence
2015-06-11, Visionen, Hus B, Campus Valla, Linköping, 10:15 (English)
Available from: 2015-05-04 Created: 2015-04-29 Last updated: 2015-05-19Bibliographically approved

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