$E$-optimality conditions and Wolfe $E$-duality for $E$-differentiable vector optimization problems with inequality and equality constraints

Antczak, Tadeusz ¹ ; Abdulaleem, Najeeb ²

¹ Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90--238 Lodz, Poland
² Department of Mathematics, Hadhramout University, P. O. BOX: (50511-50512), Al-Mahrah, Yemen

Journal of nonlinear sciences and its applications, Tome 12 (2019) no. 11, p. 745-764.

Résumé

In this paper, a nonconvex vector optimization problem with both inequality and equality constraints is considered. The functions constituting it are not necessarily differentiable, but they are $E$-differentiable. The so-called $E$-Fritz John necessary optimality conditions and the so-called $E$-Karush-Kuhn-Tucker necessary optimality conditions are established for the considered $E$-differentiable multiobjective programming problems with both inequality and equality constraints. Further, the sufficient optimality conditions are derived for such nonconvex nonsmooth vector optimization problems under (generalized) $E$-convexity. The so-called vector $E$-Wolfe dual problem is defined for the considered $E$-differentiable multiobjective programming problem with both inequality and equality constraints and several dual theorems are established also under (generalized) $E$-convexity hypotheses.

Détail

DOI : 10.22436/jnsa.012.11.06

Classification : 90C26, 90C29, 90C30, 90C46, 90C47
Keywords: \(E\)-differentiable function, \(E\)-Fritz John necessary optimality conditions, \(E\)-Karush-Kuhn-Tucker necessary optimality conditions, \(E\)-Wolfe duality, \(E\)-convex function

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