Polynomial mathematical programs with equilibrium constraints and semidefinite programming relaxations

TL;DR

This paper introduces a hierarchy of semidefinite programming relaxations to find global solutions for polynomial mathematical programs with equilibrium constraints, demonstrating convergence and efficiency through numerical experiments.

Contribution

It develops a novel SDP relaxation hierarchy for polynomial equilibrium constrained problems and proves its convergence to global minimizers.

Findings

The hierarchy converges to the global minimum.

Numerical experiments show the method's efficiency.

The approach effectively solves polynomial equilibrium constrained problems.

Abstract

This paper focuses on the study of a mathematical program with equilibrium constraints, where the objective and the constraint functions are all polynomials. We present a method for finding its global minimizers and global minimum using a hierarchy of semidefinite programming (SDP) relaxations and prove the convergence result for the method. Numerical experiments are presented to show the efficiency of the proposed algorithm.