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E-differentiable minimax programming under E-convexity

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Abstract

In this paper, a new class of minimax programming problems is considered in which the functions involved are E-differentiable. The so-called parametric and nonparametric necessary E-optimality conditions are derived for the considered E-differentiable minimax programming problem. Further, sufficient optimality conditions are established for such nondifferentiable extremum problems under E-convexity hypotheses. Moreover, the example of a nonsmooth minimax programming problem with E-differentiable functions is given to illustrate the aforesaid results. Furthermore, the so-called Mond-Weir E-dual problem and Wolfe E-dual problem are defined for the considered E-differentiable minimax programming problem and several E-duality theorems are established also under appropriate E-convexity hypotheses.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, University of Łódź, Banacha 22, 90-238, Lodz, Poland

    Tadeusz Antczak

  2. Department of Mathematics, Hadhramout University, P.O. BOX 50511-50512, Al-Mahrah, Yemen

    Najeeb Abdulaleem

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  1. Tadeusz Antczak
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  2. Najeeb Abdulaleem
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Correspondence to Najeeb Abdulaleem.

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Antczak, T., Abdulaleem, N. E-differentiable minimax programming under E-convexity. Ann Oper Res 300, 1–22 (2021). https://doi.org/10.1007/s10479-020-03925-w

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