an:06316322
Zbl 1291.90167
Riener, Cordian; Theobald, Thorsten; Andr??n, Lina Jansson; Lasserre, Jean B.
Exploiting symmetries in SDP-relaxations for polynomial optimization
EN
Math. Oper. Res. 38, No. 1, 122-141 (2013).
00328971
2013
j
90C22 90C26 14P05 05E10
polynomial optimization; semidefinite programming; semidefinite relaxation symmetry; symmetric group; constrained optimization
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.