Generalized differential properties of the Auslender gap function for variational inequalities

In this note, the Auslender gap function, which is used to formulate a variational inequality into an equivalent minimization problem, is shown to be differentiable in the generalized sense and has a lower contingent derivative under suitable conditions. This enables us to establish necessary and su...

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Bibliographic Details
Published inJournal of optimization theory and applications Vol. 124; no. 3; pp. 739 - 749
Main Authors LI, S. J, HOU, S. H, CHEN, G. Y
Format Journal Article
LanguageEnglish
Published New York, NY Springer 01.03.2005
Springer Nature B.V
Subjects
Applied sciences
Exact sciences and technology
Inequality
Mathematical functions
Mathematical programming
Operational research and scientific management
Operational research. Management science
Optimization
Science
Studies
Existence condition
gap functions
Existence of solution
Variational inequality
Minimization
lower contingent derivatives
Variational inequalities
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Summary:In this note, the Auslender gap function, which is used to formulate a variational inequality into an equivalent minimization problem, is shown to be differentiable in the generalized sense and has a lower contingent derivative under suitable conditions. This enables us to establish necessary and sufficient conditions for the existence of a solution to problems of variational inequalities.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-004-1183-y