A filter trust region method for solving semi-infinite programming problems

摘要

This paper is concerned with numerical methods for solving a semi-infinite programming problem. We first reformulate the KKT system derived from the problem into a system of semismooth equations by using the F-B NCP function. Under some conditions, a solution of the system of semismooth equations is a solution of the problem. Then we develop a filter-trust-region method for solving this system of semismooth equations. An advantage of the proposed method is that at each iteration, only a system of linear equations is solved. We prove that under standard assumptions, the iterate sequence generated by this proposed method converges globally and superlinearly. Numerical tests are also reported.