E-differentiable minimax programming under E-convexity

Tadeusz Antczak () and Najeeb Abdulaleem ()
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Tadeusz Antczak: University of Łódź
Najeeb Abdulaleem: Hadhramout University

Annals of Operations Research, 2021, vol. 300, issue 1, No 1, 22 pages

Abstract: 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.

Keywords: Minimax programming; E-differentiable function; E-optimality conditions; E-duality; E-convex function (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10479-020-03925-w

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