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Comparison of Two Structure-Exploiting Optimization Algorithms for Integral Quadratic Constraints
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
University of California, CA, USA.
2003 (English)Report (Other academic)
Abstract [en]

As the semidefinite programs that result from integral quadratic contstraints are usually large it is important to implement efficient algorithms. The interior-point algorithms in this paper are primal-dual potential reduction methods and handle multiple constraints. Two approaches are made. For the first approach the computational cost is dominated by a least-squares problem that has to be solved in each iteration. The least squares problem is solved using an iterative method, namely the conjugate gradient method. The computational effort for the second approach is dominated by forming a linear system of equations. This systems of equations is used to compute the search direction in each iteration. If the number of variables are reduced by solving a smaller subproblem the resulting system has a very nice structure and can be solved efficiently. The first approach is more efficient for larger problems but is not as numerically stable.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2003. , 14 p.
Series
LiTH-ISY-R, ISSN 1400-3902 ; 2502
Keyword [en]
Interior-point algorithms, Semidefinite programs, Integral quadratic constraints
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-55925ISRN: LiTH-ISY-R-2502OAI: oai:DiVA.org:liu-55925DiVA: diva2:316809
Funder
Swedish Research Council, 271-2000-770
Available from: 2010-04-30 Created: 2010-04-30 Last updated: 2014-08-12Bibliographically approved

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Hansson, AndersWallin, Ragnar

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
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