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Exploiting symmetries in SDP-relaxations for polynomial optimization

Cordian Riener (cordian.riener***at***aalto.fi)
Thorsten Theobald (theobald***at***math.uni-frankfurt.de)
Lina Jansson Andrén (lina.andren***at***math.umu.se)
Jean Bernard Lasserre (lasserre***at***laas.fr)

Abstract: In this paper we study various approaches for exploiting symmetries in polynomial optimization problems within the framework of semi definite 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 in the geometric quotient.

Keywords: Global optimization; SDP-relaxations; symmetries

Category 1: Global Optimization (Theory )

Category 2: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Citation: Mathematics of Operations Research 38 (1), p 122-141, 2013

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Entry Submitted: 09/16/2006
Entry Accepted: 09/18/2006
Entry Last Modified: 07/11/2013

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