Variants of the Ekeland variational principle for a set-valued map involving the Clarke normal cone
type: Item
instance of: scholarly article
title: Variants of the Ekeland variational principle for a set-valued map involving the Clarke normal cone
zbMATH Open document ID: 1089.49031
published in: Journal of Mathematical Analysis and Applications
publication date: 2006-03-29T00:00:00Z
review text: In this paper it is extended Ekeland's variational principle to vector-set-valued maps \(F\). The author uses the Clarke normal cone of the graph of \(F\), which enables him to establish sufficient conditions on \(F\) in order to have a weak minimizer or a properly positive minimizer when the Palais-Smale compactness condition is fulfilled. The proof of the main result is based on the Clarke-Rockafellar theorem on the generalized gradient of a sum of nonsmooth functions.
reviewed by: Vicenţiu D. Rădulescu
Mathematics Subject Classification ID: 49K27
Mathematics Subject Classification ID: 49J52
Mathematics Subject Classification ID: 49J53
Mathematics Subject Classification ID: 90C29
zbMATH DE Number: 5016184
zbMATH Keywords: Ekeland variational principle
zbMATH Keywords: vector optimization
zbMATH Keywords: set-valued map
zbMATH Keywords: Clarke normal cone
zbMATH Keywords: coderivative
author: Trúóng Xuân Dúc Hā
MaRDI profile type: Publication
full work available at URL: j.jmaa.2005.04.044
OpenAlex ID: W2045446464
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DOI: 10.1016/J.JMAA.2005.04.044
description: scientific article; zbMATH DE number 5016184