Set-valued optimization problems via second-order contingent epiderivative

Abstract

In this paper, we establish second-order KKT conditions of a set-valued optimization problem and study second-order Mond-Weir, Wolfe, and mixed types duals with the help of second-order contingent epiderivative and second-order generalized cone convexity assumptions.

Sufficiency and duality of set-valued fractional programming problems via second-order contingent epiderivative

“…Das and Nahak [8]- [19] introduced the notion of ρ-cone convex set-valued maps. They established the sufficient KKT conditions and studied the duality results for various types of set-valued optimization problems under contingent epiderivative and ρ-cone convexity assumptions.…”

“…Das and Nahak [9] introduced second-order ρ-cone convexity of set-valued maps via second-order contingent epiderivative.…”

“…Das and Nahak [9] constructed a set-valued map F : R → 2 R 2 , which is secondorder ρ-R 2 + -convex for some ρ, but is not second-order R m + -convex.…”

“…They also studied the duality results of parametric, Mond-Weir, Wolfe, and mixed types for the problem. Later, they [9] established the sufficient KKT optimality conditions of set-valued optimization problems under generalized convexity assumptions and higher-order contingent derivative assumptions. They also proved weak, strong, and converse duality theorems of Mond-Weir, Wolfe and mixed types.…”

On Constrained Set-Valued Semi-Infinite Programming Problems with ρ-Cone Arcwise Connectedness

“…Das and Nahak [22][23][24][25] and Treanţȃ and Das [26] introduced the notion of ρ-cone convexity of set-valued maps. They establish the sufficient KKT optimality conditions of set-valued optimization problems under contingent epiderivative and ρ-cone convexity assumptions.…”