Exploiting symmetries in SDP-relaxations for polynomial optimization

Abstract. We consider the issue of exploiting symmetries in the hierarchy of semidefinite programming relaxations recently introduced in polynomial optimization. We focus on problems where either the symmetric or the cyclic group is acting on the variables and extend the representation-theoretical methods of Gatermann and Parrilo to constrained polynomial optimization problems. Moreover, we also propose methods to efficiently compute lower and upper bounds for the subclass of problems where the objective function and the constraints are described in terms of power sums.

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Cordian Riener, Thorsten Theobald, Lina Jansson Andrén, Jean B. Lasserre
• Keywords: CORR 2011, Education, Polynomial Optimization, Polynomial Optimization Problems, Semidefinite Programming Relaxations