On Lipschitz Semicontinuity Properties of Variational Systems with Application to Parametric Optimization

In this paper, two properties of recognized interest in variational analysis, known as Lipschitz lower semicontinuity and calmness, are studied with reference to a general class of variational systems, i.e. to solution mappings to parameterized generalized equations. In the consideration of the metr...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 162; no. 1; pp. 47 - 78
Main Author: Uderzo, A.
Format: Journal Article
Language:English
Published: Boston Springer US 01.07.2014
Springer Nature B.V
Subjects:
Analysis
Applications of Mathematics
Applied mathematics
Calculus of Variations and Optimal Control; Optimization
Constraints
Derivatives
Engineering
Mapping
Mathematical analysis
Mathematical programming
Mathematics
Mathematics and Statistics
Metric space
Operations Research/Decision Theory
Optimization
Recognition
Stability analysis
Studies
Theory of Computation
Lipschitz lower semicontinuity
Strict outer slope
Parametric constrained optimization
Generalized equation
Implicit multifunction
Fréchet subdifferential and coderivative
Calmness
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary:In this paper, two properties of recognized interest in variational analysis, known as Lipschitz lower semicontinuity and calmness, are studied with reference to a general class of variational systems, i.e. to solution mappings to parameterized generalized equations. In the consideration of the metric nature of such properties, some related sufficient conditions are established, which are expressed via nondegeneracy conditions on derivative-like objects appropriate for a metric space analysis. For certain classes of generalized equations in Asplund spaces, it is shown how such conditions can be formulated by using the Fréchet coderivative of the field and the derivative of the base. Applications to the stability analysis of parametric constrained optimization problems are proposed.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-013-0455-9