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Low-Rank Exploitation in Semidefinite Programming for Control
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.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
2010 (English)In: Proceedings of the 2010 IEEE International Symposium on Computer-Aided Control System Design, 2010, 24-28 p.Conference paper, Published paper (Refereed)
Abstract [en]

Many control related problems can be cast as semidefinite programs but, even though there exist polynomial time algorithms and good publicly available solvers, the time it takes to solve these problems can be long. Something many of these problems have in common, is that some of the variables enter as matrix valued variables. This leads to a low-rank structure in the basis matrices which can be exploited when forming the Newton equations. In this paper, we describe how this can be done, and show how our code can be used when using SDPT3. The idea behind this is old and is implemented in LMI Lab, but we show that when using a modern algorithm, the computational time can be reduced. Finally, we describe how the modeling language YALMIP is changed in such a way that our code can be interfaced using standard YALMIP commands, which greatly simplifies for the user.

Place, publisher, year, edition, pages
2010. 24-28 p.
Keyword [en]
Semidefinite programming, Structure exploitation, Mathematical programming, Matrix algebra
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-63294DOI: 10.1109/CACSD.2010.5612835ISBN: 978-1-4244-5354-2 (print)ISBN: 978-1-4244-5355-9 (print)OAI: oai:DiVA.org:liu-63294DiVA: diva2:377904
Conference
2010 IEEE International Symposium on Computer-Aided Control System Design, Yokohama, Japan, 2-10 September, 2010
Available from: 2010-12-15 Created: 2010-12-15 Last updated: 2013-07-09

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Falkeborn, RikardLöfberg, JohanHansson, Anders

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
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  • asciidoc
  • rtf