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Symmetries in SDP-based relaxations for constrained polynomial optimization

Wednesday, March 21, 2007 - 11:15am - 12:15pm
Keller 3-180
Thorsten Theobald (Johann Wolfgang Goethe-Universität Frankfurt)
We consider the issue of exploiting symmetries in the hierarchy of semidefinite programming relaxations recently introduced in polynomial optimization. After providing the necessary background 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.

(Joint work with L. Jansson, J.B. Lasserre and C. Riener)