Variants of the Ekeland Variational Principle for a set-valued map involving the Clarke Normal Cone

In this paper we present two set-valued variants of the Ekeland variational principle involving the Clarke normal cone and establish sufficient conditions for a set-valued map to have a weak minimizer or a properly positive minimizer when it satisfies Palais–Smale type conditions.

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Bibliographic Details
Published in:Journal of mathematical analysis and applications Vol. 316; no. 1; pp. 346 - 356
Main Author: Ha, Truong Xuan Duc
Format: Journal Article
Language:English
Published: San Diego, CA Elsevier Inc 01.04.2006
Elsevier
Subjects:
Calculus of variations and optimal control
Clarke's normal cone
Coderivative
Ekeland's variational principle
Exact sciences and technology
Global analysis, analysis on manifolds
Mathematical analysis
Mathematics
Sciences and techniques of general use
Set-valued map
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Vector optimization
Ekeland's variational principle
Set-valued map
Clarke's normal cone
Coderivative
Vector optimization
Sufficient condition
Mathematical analysis
Set-valued mapping
Optimization method
Variational principle
Palais Smale condition
Clarke normal cone
ISSN:0022-247X, 1096-0813
Online Access:Get full text
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Description
Summary:In this paper we present two set-valued variants of the Ekeland variational principle involving the Clarke normal cone and establish sufficient conditions for a set-valued map to have a weak minimizer or a properly positive minimizer when it satisfies Palais–Smale type conditions.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2005.04.044