Optimization Problems With Difference of Set-Valued Maps Under Generalized Cone Convexity

Abstract

In this paper, we establish the necessary and sufficient Karush-Kuhn-Tucker (KKT) conditions for an optimization problem with difference of set-valued maps under generalized cone convexity assumptions. We also study the duality results of Mond-Weir (M W D), Wolfe (W D) and mixed (Mix D) types for the weak solutions of the problem (P).

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.…”