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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Veröffentlicht in:Nonlinear analysis Jg. 86; S. 159 - 180
Hauptverfasser: Mordukhovich, B.S., Nghia, T.T.A.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Ltd 01.07.2013
Schlagworte:
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
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Beschreibung
Zusammenfassung: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.
Bibliographie:ObjectType-Article-2
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ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2013.03.014