Optimality Conditions for Set-Valued Minimax Programming Problems via Second-Order Contingent Epiderivative

Abstract

In this paper, we establish second-order KKT sufficient optimality conditions of a set-valued minimax programming problem via second-order contingent epiderivative. We formulate second-order duals of Mond-Weir type, Wolfe type, and mixed type and further present corresponding duality results between the stated primal and dual problems under the assumption of second-order generalized cone convexity.

Set-valued optimization problems via second-order contingent epiderivative

“…Das and Nahak [5,6,7,8,9,10,11,12,13,14,15] introduced the notion of ρ-cone convex set-valued maps. They establish the sufficient KKT conditions and study the duality results for various types of set-valued optimization problems under contingent epiderivative and ρ-cone convexity assumptions.…”

Parametric Set-Valued Optimization Problems Under Generalized Cone Convexity

“…Das and Nahak [4,5,6,7,8,9,10,11,12,13,14,15] introduced the notion of ρ-cone convex set-valued maps. They establish the sufficient KKT conditions and study the duality results for various types of set-valued optimization problems under contingent epiderivative and ρ-cone convexity assumptions.…”

Set-valued minimax programming problems under higher-order σ-arcwisely connectivity

“…The concept of σ-convexity of SVMs was proposed by Das and Nahak [13,16]. They established the KKT criteria of sufficient optimality and developed the dual results for different SVOP types under the assumptions of contingent epidifferentiation and σ-convexity.…”