Quasiconvex sum-of-squares programming

Peter J Seiler Jr, Gary J. Balas

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

23 Scopus citations

Abstract

A sum-of-squares program is an optimization problem with polynomial sum-of-squares constraints. The constraints and the objective function are affine in the decision variables. This paper introduces a generalized sum-of-squares programming problem. This generalization allows one decision variable to enter bilinearly in the constraints. The bilinear decision variable enters the constraints in a particular structured way. The objective function is the single bilinear decision variable. It is proved that this formulation is quasiconvex and hence the global optima can be computed via bisection. Many nonlinear analysis problems can be posed within this framework and two examples are provided.

Original languageEnglish (US)
Title of host publication2010 49th IEEE Conference on Decision and Control, CDC 2010
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3337-3342
Number of pages6
ISBN (Print)9781424477456
DOIs
StatePublished - 2010
Event49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, United States
Duration: Dec 15 2010Dec 17 2010

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370

Conference

Conference49th IEEE Conference on Decision and Control, CDC 2010
Country/TerritoryUnited States
CityAtlanta
Period12/15/1012/17/10

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