# 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.

## Key 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.

---
Source: https://tomesphere.com/paper/1903.09534