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Duality results for interval-valued pseudoconvex optimization problem with equilibrium constraints with applications

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Abstract

This paper is devoted to constructing Wolfe and Mond–Weir dual models for interval-valued pseudoconvex optimization problem with equilibrium constraints, as well as providing weak and strong duality theorems for the same using the notion of contingent epiderivatives with pseudoconvex functions in real Banach spaces. First, we introduce the Mangasarian–Fromovitz type regularity condition and the two Wolfe and Mond–Weir dual models to such problem. Second, under suitable assumptions on the pseudoconvexity of objective and constraint functions, weak and strong duality theorems for the interval-valued pseudoconvex optimization problem with equilibrium constraints and its Mond–Weir and Wolfe dual problems are derived. An application of the obtained results for the GA-stationary vector to such interval-valued pseudoconvex optimization problem on sufficient optimality is presented. We also give several examples that illustrate our results in the paper.

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Acknowledgements

The author would like to express their sincere gratitude to the two anonymous reviewers for their through and helpful reviews which significantly improved the quality of the paper. Further the author acknowledges the editors for sending our manuscript to reviewers.

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Authors and Affiliations

  1. Department of Mathematics, Quang Nam University, Tamky, Vietnam

    Tran Van Su

  2. Department of Basic Sciences, Thai Nguyen University of Information and Communication Technology, Thai Nguyen, Vietnam

    Dieu Hang Dinh

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  1. Tran Van Su
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  2. Dieu Hang Dinh
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Correspondence to Tran Van Su.

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Communicated by Gabriel Haeser.

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Van Su, T., Dinh, D.H. Duality results for interval-valued pseudoconvex optimization problem with equilibrium constraints with applications. Comp. Appl. Math. 39, 127 (2020). https://doi.org/10.1007/s40314-020-01153-3

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