Set-valued fractional programming problems with $ \sigma $-arcwisely connectivity

Abstract

In this paper, we determine the sufficient Karush-Kuhn-Tucker (KKT) conditions of optimality of a set-valued fractional programming problem (in short, SVFP) $\rm (FP)$ under the suppositions of contingent epidifferentiation and $ \sigma $-arcwisely connectivity. We additionally explore the results of duality of parametric $\rm (PD)$, Mond-Weir $\rm (MWD)$, Wolfe $\rm (WD)$, and mixed $\rm (MD)$ kinds for the problem $\rm (FP)$.

Keywords

• set-valued map
• convex cone
• contingent epidifferentiation
• duality