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A hybrid algorithm for linearly constrained minimax problems

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Abstract

Many real life problems can be stated as a minimax problem, such as economics, finance, management, engineering and other fields, which demonstrate the importance of having reliable methods to tackle minimax problems. In this paper, an algorithm for linearly constrained minimax problems is presented in which we combine the trust-region methods with the line-search methods and curve-search methods. By means of this hybrid technique, it avoids possibly solving the trust-region subproblems many times, and make better use of the advantages of different methods. Under weaker conditions, the global and superlinear convergence are achieved. Numerical experiments show that the new algorithm is robust and efficient.

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Acknowledgements

The authors are indebted to the editors and anonymous referees for their a number of helpful comments and suggestions that improved the quality of this manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Taiyuan Normal University, Taiyuan, 030012, P.R. China

    Fusheng Wang

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  1. Fusheng Wang
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Correspondence to Fusheng Wang.

Additional information

This work is supported by the National Natural Science Foundation of China (11171250); Educational Commission of Shanxi Province of China (20091021); Foundation of Taiyuan Normal University (A0647).

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Wang, F. A hybrid algorithm for linearly constrained minimax problems. Ann Oper Res 206, 501–525 (2013). https://doi.org/10.1007/s10479-012-1274-3

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