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Specialized fast algorithms for IQC feasibility and optimization problems
KTH, Superseded Departments, Mathematics.
KTH, Superseded Departments, Mathematics.
2004 (English)In: Automatica, ISSN 0005-1098, Vol. 40, no 2, 239-252 p.Article in journal (Refereed) Published
Abstract [en]

The conventional way to treat integral quadratic constraint (IQC) problems is to transform them into semi-definite programs (SDPs). SDPs can then be solved using interior point methods which have been proven efficient. This approach, however, is not always the most efficient since it introduces additional decision variables to the SDP, and the additional decision variables sometimes largely increase the complexity of the problem. In this paper, we demonstrate how to solve IQC problems by other alternatives. More specifically, we consider two cutting plane algorithms. We will show that in certain cases these cutting plane algorithms can solve IQC problems much faster than the conventional approach. Numerical examples, as well as some explanations from the point of view of computational complexity, are provided to support our point.

Place, publisher, year, edition, pages
2004. Vol. 40, no 2, 239-252 p.
Keyword [en]
integral quadratic constraint, cutting plane method, semidefinite, programming, stability analysis, positive real lemma, cutting plane method, complexity analysis, multiple cuts, deep
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-23114DOI: 10.1016/j.automatica.2003.09.016ISI: 000188418400006Scopus ID: 2-s2.0-0347355016OAI: oai:DiVA.org:kth-23114DiVA: diva2:341812
Note
QC 20100525 QC 20111031Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2011-10-31Bibliographically approved

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