A smoothing Levenberg–Marquardt method for generalized semi-infinite programming

Abstract

This paper is concerned with a numerical method for generalized semi-infinite programming problem. We first reformulate the generalized semi-infinite programming problem into an invariable-dimensional KKT system. Then by using perturbed Fischer–Burmeister function, we present a smoothing Levenberg–Marquardt method for solving this system of semismooth equations and show its global convergence under common conditions. Furthermore, the local superlinear convergence of the method is proved under local error bound condition. Finally, numerical results are given.