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E-differentiable minimax programming under E-convexity

Author

Listed:
  • Tadeusz Antczak

    (University of Łódź)

  • Najeeb Abdulaleem

    (Hadhramout University)

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.

Suggested Citation

  • Tadeusz Antczak & Najeeb Abdulaleem, 2021. "E-differentiable minimax programming under E-convexity," Annals of Operations Research, Springer, vol. 300(1), pages 1-22, May.
    • Handle: RePEc:spr:annopr:v:300:y:2021:i:1:d:10.1007_s10479-020-03925-w
    DOI: 10.1007/s10479-020-03925-w
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    References listed on IDEAS

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    Cited by:

    1. Tadeusz Antczak & Najeeb Abdulaleem, 2023. "On the exactness and the convergence of the $$l_{1}$$ l 1 exact penalty E-function method for E-differentiable optimization problems," OPSEARCH, Springer;Operational Research Society of India, vol. 60(3), pages 1331-1359, September.

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