### A TRUST-REGION ALGORITHM FOR SOLVING MINI-MAX PROBLEM

Bothina El-Sobky, Abdallah Abotahoun

1. Department of Mathematics, Alexandria University, Alexandria, Egypt
• Received:2016-08-29 Revised:2017-03-02 Online:2018-11-15 Published:2018-11-15
• Supported by:

The authors would like to thank the anonymous referees for their valuable comments and suggestions which have helped to greatly improve this paper.

Bothina El-Sobky, Abdallah Abotahoun. A TRUST-REGION ALGORITHM FOR SOLVING MINI-MAX PROBLEM[J]. Journal of Computational Mathematics, 2018, 36(6): 776-791.

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.

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