Exploiting symmetries in SDP-relaxations for polynomial optimization
For researchers in polynomial optimization, this work provides practical techniques to reduce computational costs by leveraging symmetries, though it is incremental in nature.
This paper develops methods to exploit symmetries in polynomial optimization problems using semidefinite programming relaxations, focusing on constrained problems with symmetric group actions. It introduces block decomposition and efficient computation in the geometric quotient to reduce computational complexity.
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.