Generalized Semi-infinite Polynomial Optimization and Semidefinite Programming Relaxations

Abstract

This paper focuses on the study of a generalized semi-infinite programming, where the objective and the constraint functions are all real polynomials. We present a method for finding its global minimizers and global minimum using a hierarchy of semidefinite programming relaxations and prove the convergence result for the method. Numerical experiments are presented to show the efficiency of the proposed algorithm.