On Some Regularity Properties in Variational Analysis

Some properties, connected with recent generalizations of the classic notion of Lipschitz continuity for multifunctions, are investigated with reference to variational systems, that is to solution maps associated to parametrized generalized equations. The latter ones are a convenient framework to ad...

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Bibliographic Details
Published in:Set-Valued and Variational Analysis Vol. 17; no. 4; pp. 409 - 430
Main Author: Uderzo, Amos
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.12.2009
Subjects:
Analysis
Mathematics
Mathematics and Statistics
Optimization
Generalized equations
49J52
Open covering
Variational principle
Primary: 49J53
Lipschitz-likeness
Metric regularity
Secondary: 47H04
54C60
ISSN:1877-0533, 1572-932X, 1877-0541
Online Access:Get full text
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Summary:Some properties, connected with recent generalizations of the classic notion of Lipschitz continuity for multifunctions, are investigated with reference to variational systems, that is to solution maps associated to parametrized generalized equations. The latter ones are a convenient framework to address several questions, mainly related to the stability and sensitivity analysis, arising in mathematical programming, optimal control, equilibrium and variational inequality theory. Global and local criteria for metric regularity and Lipschitz-likeness of variational systems are obtained. Some applications to the exact penalization of mathematical programs with equilibrium constraints and to the Lipschitzian stability of fixed points for multivalued contractions are then considered.
ISSN:1877-0533
1572-932X
1877-0541
DOI:10.1007/s11228-009-0121-4