On Constrained Set-Valued Semi-Infinite Programming Problems with <i>ρ</i>-Cone Arcwise Connectedness

On Constrained Set-Valued Semi-Infinite Programming Problems with <i>ρ</i>-Cone Arcwise Connectedness

In this paper, we establish sufficient Karush–Kuhn–Tucker (for short, KKT) conditions of a set-valued semi-infinite programming problem (SP) via the notion of contingent epiderivative of set-valued maps. We also derive duality results of Mond–Weir (MWD), Wolfe (WD), and mixed (MD) types of the probl...

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Bibliographic Details
Main Authors: Koushik Das, Savin Treanţă
Format: Article
Language:English
Published: MDPI AG 2021-11-01
Series:Axioms
Subjects:
set-valued map
convex cone
duality
contingent epiderivative
Online Access:https://www.mdpi.com/2075-1680/10/4/302
Description
Summary:In this paper, we establish sufficient Karush–Kuhn–Tucker (for short, KKT) conditions of a set-valued semi-infinite programming problem (SP) via the notion of contingent epiderivative of set-valued maps. We also derive duality results of Mond–Weir (MWD), Wolfe (WD), and mixed (MD) types of the problem (SP) under <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>-cone arcwise connectedness assumptions.
ISSN:2075-1680

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