An Ellipsoid Algorithm for linear optimization with uncertain LMI constraints

Armin Ataei, Qian Wang

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

In this paper, an efficient algorithm based on the ellipsoid method is proposed to solve a linear optimization problem over a set of uncertain Linear Matrix Inequalities (LMIs). First, an Ellipsoid Algorithm (EA) with deep cuts is introduced for solving the set of uncertain LMIs. The proposed ellipsoid algorithm is shown to converge to a probabilistically feasible point with high confidence level and in fewer iterations compared to other EA methods. Then, through a set of new cuts, the objective function is minimized while maintaining the probabilistic feasibility of the solution.

Original languageEnglish (US)
Title of host publication2012 American Control Conference, ACC 2012
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages857-862
Number of pages6
ISBN (Print)9781457710957
DOIs
StatePublished - Jan 1 2012
Event2012 American Control Conference, ACC 2012 - Montreal, QC, Canada
Duration: Jun 27 2012Jun 29 2012

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619

Other

Other2012 American Control Conference, ACC 2012
CountryCanada
CityMontreal, QC
Period6/27/126/29/12

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

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    Ataei, A., & Wang, Q. (2012). An Ellipsoid Algorithm for linear optimization with uncertain LMI constraints. In 2012 American Control Conference, ACC 2012 (pp. 857-862). [6315611] (Proceedings of the American Control Conference). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/acc.2012.6315611