A global approach for generalized semi-infinte programs with polyhedral parameter sets

TL;DR

This paper introduces a novel semidefinite programming approach for solving generalized semi-infinite programs with polyhedral parameters, utilizing KKT conditions and partial Lagrange multipliers, with demonstrated efficiency in practical applications.

Contribution

It presents a new method transforming GSIPs into disjunctive programs using KKT conditions and partial Lagrange multipliers, along with a semidefinite algorithm and convergence analysis.

Findings

The proposed method is efficient in numerical experiments.

It performs well in gemstone cutting applications.

The approach is effective for robust control problems.

Abstract

This paper studies generalized semi-infinite programs (GSIPs) defined with polyhedral parameter sets. Assume these GSIPs are given by polynomials. We propose a new approach to solve them as a disjunctive program. This approach is based on the Karush-Kuhn-Tucker (KKT) conditions of the robust constraint and a technique called partial Lagrange multiplier expressions. We summarize a semidefinite algorithm and study its convergence properties. Numerical experiments are given to show the efficiency of our method. In addition, we checked its performance in gemstone cutting and robust control applications.