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An active-set algorithm and a trust-region approach in constrained minimax problem

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Abstract

In this paper, we propose an algorithm to solve a finite minimax problem with side constraints. An active-set strategy is used in the algorithm to transform inequality constraints to equality constraints. This allows the use of the well-developed techniques for solving the equality constrained optimization problems. A trust-region globalization strategy is added to the proposed algorithm to ensure global convergence. A projected Hessian technique is used in the algorithm to overcome the difficulty of having an infeasible trust-region subproblem. A global convergence theory for the proposed algorithm is presented under standard assumptions. Finally, numerical experiments are reported to indicate that the new algorithm performs efficiently in practice.

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Acknowledgements

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

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt

    B. EL-Sobky & A. W. Aboutahoun

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  1. B. EL-Sobky
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  2. A. W. Aboutahoun
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Correspondence to B. EL-Sobky.

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Communicated by José Mario Martínez (Associate Editor).

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EL-Sobky, B., Aboutahoun, A.W. An active-set algorithm and a trust-region approach in constrained minimax problem. Comp. Appl. Math. 37, 2605–2631 (2018). https://doi.org/10.1007/s40314-017-0468-3

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  • DOI: https://doi.org/10.1007/s40314-017-0468-3

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