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.

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

“…Let π : α → 2 β be a SVM, M ⊆ domain(π), (p ′ , q ′ ), (p 1 , q 1 ), ..., [14] Take into consideration that α, β are RNSs, M is an arcwisely connected subset of α, Q is a convex cone of β that is also pointed as well as solid, σ ∈ R, e ∈ int(Q), and π : α → 2 β is a SVM, along with M ⊆ domain(π). Take into consideration that π is generalized contingent epiderivable of ρ-th order at (p ′ , q ′ ) for (p…”

“…Higher-order contingent epi-derivative was developed by Das and Nahak [14] to introduce higher-order σ-cone convexity of SVMs.…”

“…Definition 2.11 [14] Take that into account α, β are RNSs, M is a subset of α that is not empty, Q is a convex cone of β that is also pointed as well as solid, σ ∈ R, e ∈ int(Q), and π : α → 2 β is a SVM, along with M ⊆ domain(π). Suppose that (p ′ , q ′ ), (p 1 , q 1 ), ...,…”