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

Abstract

In this paper, we establish second-order sufficient KKT optimality conditions of a set-valued fractional programming problem under second-order generalized cone convexity assumptions. We also prove duality results between the primal problem and second-order dual problems of parametric, Mond-Weir, Wolfe, and mixed types via the notion of second-order contingent epiderivative.

Keywords

• convex cone
• set-calued map
• contingent epiderivative
• duality