Higher-order tangent epiderivatives and applications to duality in set-valued optimization
type: Item
instance of: scholarly article
title: Higher-order tangent epiderivatives and applications to duality in set-valued optimization
zbMATH Open document ID: 1483.46043
author: Tran Thien Khai
author: Nguyen Manh Truong Giang
author: Nguyen Le Hoang Anh
published in: Positivity
publication date: 2021-12-02T00:00:00Z
review text: Let \(X,Y\) be real Banach spaces and \(C\) a pointed closed convex cone in \(Y\). For a set-valued mapping \(F:X\to 2^Y\) one defines the graph and the epigraph of \(F\) by \[\mathrm{gr}\, F:=\{(x,y)\in X\times Y:y\in F(x)\}\] and \[\mathrm{epi}_C F=\{(x,y)\in X\times Y: y\in F(x)+C\}\,,\] respectively. Two approaches are known to define contingent derivatives of \(F\) -- using linear approximation of its graph or of its epigraph. In the present paper the authors adopt the second approach -- they consider higher-order tangent epiderivatives, study their properties and give applications to set-valued optimization, namely duality for a mixed constrained optimization problem.
Mathematics Subject Classification ID: 46G05
Mathematics Subject Classification ID: 54C60
Mathematics Subject Classification ID: 90C46
zbMATH DE Number: 7437469
zbMATH Keywords: higher-order tangent epiderivative
zbMATH Keywords: set-valued map
zbMATH Keywords: duality
zbMATH Keywords: optimization problem with mixed constraints
zbMATH Keywords: Benson properly efficient solution
reviewed by: Stefan Cobzaş
MaRDI profile type: Publication
full work available at URL: s11117-021-00838-1
OpenAlex ID: W3165959022
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DOI: 10.1007/S11117-021-00838-1
description: scientific article; zbMATH DE number 7437469