Second-order variational analysis and characterizations of tilt-stable optimal solutions in infinite-dimensional spaces

The paper is devoted to developing second-order tools of variational analysis and their applications to characterizing tilt-stable local minimizers of constrained optimization problems infinite-dimensional spaces with many results new also in finite-dimensional settings. The importance of tilt stabi...

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Bibliographic Details
Published in:	Nonlinear analysis Vol. 86; pp. 159 - 180
Main Authors:	Mordukhovich, B.S., Nghia, T.T.A.
Format:	Journal Article
Language:	English
Published:	Elsevier Ltd 01.07.2013
Subjects:	Camber First-order and second-order generalized differentiation Lipschitzian stability Second-order growth Strong metric regularity Variational analysis and optimization Variational analysis and optimization Second-order growth Lipschitzian stability Strong metric regularity First-order and second-order generalized differentiation
ISSN:	0362-546X, 1873-5215
Online Access:	Get full text
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Summary:	The paper is devoted to developing second-order tools of variational analysis and their applications to characterizing tilt-stable local minimizers of constrained optimization problems infinite-dimensional spaces with many results new also in finite-dimensional settings. The importance of tilt stability has been well recognized from both theoretical and numerical aspects of optimization. Based on second-order generalized differentiation, we obtain qualitative and quantitative characterizations of tilt stability in general frameworks of constrained optimization and establish its relationships with strong metric regularity of subgradient mappings and uniform second-order growth. The results obtained are applied to deriving new necessary and sufficient conditions for tilt-stable minimizers in problems of nonlinear programming with twice continuously differentiable data in Hilbert spaces.
Bibliography:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	0362-546X 1873-5215
DOI:	10.1016/j.na.2013.03.014