Semidefinite Relaxations for Semi-Infinite Polynomial Programming
Li Wang
UC San Diego
Abstract:
We study how to solve semi-infinite polynomial programming
(SIPP) problems by semidefinite relaxation method. We first introduce two
SDP relaxation methods for solving polynomial optimization problems with
finitely many constraints. Then we propose an exchange algorithm with SDP
relaxations to solve SIPP problems with compact index set. At last, we
extend the proposed method to SIPP problems with noncompact index set via
homogenization. Numerical results show that the algorithm is efficient in
practice.