A Trust-Region Algorithm for Solving Mini-Max Problem

Abstract

In this paper, we propose an algorithm for solving inequality constrained mini-max optimization problem. In this algorithm, an active set strategy is used together with multiplier method to convert the inequality constrained mini-max optimization problem into unconstrained optimization problem. A trust-region method is a well-accepted technique in constrained optimization to assure global convergence and is more robust when they deal with rounding errors. One of the advantages of trust-region method is that it does not require the objective function of the model to be convex. 

A global convergence analysis for the proposed algorithm is presented under some conditions. To show the efficiency of the algorithm numerical results for a number of test problems are reported.