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Nondifferentiable minimax programming problems with applications

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Abstract

This paper is devoted to the study of optimality conditions and duality in nondifferentiable minimax programming problems and applications. Employing some advanced tools of variational analysis and generalized differentiation, we establish new necessary conditions for optimal solutions of a minimax programming problem involving inequality and equality constraints. Sufficient conditions for the existence of such solutions to the considered problem are also obtained by way of \(L\)-invex-infine functions. We state a dual problem to the primal one and explore weak, strong and converse duality relations between them. In addition, some of these results are applied to a nondifferentiable multiobjective optimization problem.

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Acknowledgments

The authors would like to thank the editor and the referees for valuable comments and suggestions.

Conflict of interest

The authors declare that they have no potential conflict of interest.

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Authors and Affiliations

  1. Department of Mathematics and Applications, Saigon University, 273 An Duong Vuong Street, Ward 3, District 5, Ho Chi Minh City, Vietnam

    Thai Doan Chuong

  2. Department of Applied Mathematics, Pukyong National University, Busan, 608-737, Korea

    Do Sang Kim

Authors
  1. Thai Doan Chuong
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  2. Do Sang Kim
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Corresponding author

Correspondence to Do Sang Kim.

Additional information

This work was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education Science and Technology (NRF-2013R1A1A2A10008908) and by the Vietnam National Foundation for Science and Technology Development (NAFOSTED: No. 101.01-2014.17).

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Chuong, T.D., Kim, D.S. Nondifferentiable minimax programming problems with applications. Ann Oper Res 251, 73–87 (2017). https://doi.org/10.1007/s10479-015-1843-3

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  • DOI: https://doi.org/10.1007/s10479-015-1843-3

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