Exploiting Symmetries in SDP-Relaxations for Polynomial Optimization

Authors:
Cordian Riener;Thorsten Theobald;Lina Jansson Andrén;Jean B. Lasserre
Affiliations:
Fachbereich Mathematik und Statistik, Universität Konstanz, 78457 Konstanz, Germany;FB 12 -- Institut für Mathematik, Goethe-Universität, 60054 Frankfurt am Main, Germany;Department of Mathematics and Math. Statistics, Umeå Universitet, 901 87 Umeå, Sweden;LAAS-CNRS and Institute of Mathematics, 31077 Toulouse Cedex 4, France
Venue:
Mathematics of Operations Research
Year:
2013

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Abstract

In this paper we study various approaches for exploiting symmetries in polynomial optimization problems within the framework of semidefinite programming relaxations. Our special focus is on constrained problems especially when the symmetric group is acting on the variables. In particular, we investigate the concept of block decomposition within the framework of constrained polynomial optimization problems, show how the degree principle for the symmetric group can be computationally exploited, and also propose some methods to efficiently compute the geometric quotient.