×

zbMATH — the first resource for mathematics

Exploiting symmetries in SDP-relaxations for polynomial optimization. (English) Zbl 1291.90167
Summary: 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.

MSC:
90C22 Semidefinite programming
90C26 Nonconvex programming, global optimization
14P05 Real algebraic sets
05E10 Combinatorial aspects of representation theory
Software:
SeDuMi
PDF BibTeX XML Cite
Full Text: DOI arXiv