Variational Stability and Marginal Functions via Generalized Differentiation

Robust Lipschitzian properties of set-valued mappings and marginal functions play a crucial role in many aspects of variational analysis and its applications, especially for issues related to variational stability and optimization. We develop an approach to variational stability based on generalized...

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Published in:Mathematics of operations research Vol. 30; no. 4; pp. 800 - 816
Main Authors: Mordukhovich, Boris S, Nam, Nguyen Mau
Format: Journal Article
Language:English
Published: Linthicum INFORMS 01.11.2005
Institute for Operations Research and the Management Sciences
Subjects:
Analysis
Banach space
Calculus
Chain rule
Differential calculus
Differential equations
generalized differentiation
Lipschitz condition
marginal and value functions
Mathematical analysis
Mathematical differentiation
Mathematical functions
Mathematical theorems
Operations research
Optimization
optimization and variational analysis
Property composition
robust stability and sensitivity
Sensitivity analysis
Studies
United States
ISSN:0364-765X, 1526-5471
Online Access:Get full text
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Abstract Robust Lipschitzian properties of set-valued mappings and marginal functions play a crucial role in many aspects of variational analysis and its applications, especially for issues related to variational stability and optimization. We develop an approach to variational stability based on generalized differentiation. The principal achievements of this paper include new results on coderivative calculus for set-valued mappings and singular subdifferentials of marginal functions in infinite dimensions with their extended applications to Lipschitzian stability. In this way we derive efficient conditions ensuring the preservation of Lipschitzian and related properties for set-valued mappings under various operations, with the exact bound/modulus estimates, as well as new sufficient conditions for the Lipschitz continuity of marginal functions.
AbstractList Robust Lipschitzian properties of set-valued mappings and marginal functions play a crucial role in many aspects of variational analysis and its applications, especially for issues related to variational stability and optimization. We develop an approach to variational stability based on generalized differentiation. The principal achievements of this paper include new results on coderivative calculus for set-valued mappings and singular subdifferentials of marginal functions in infinite dimensions with their extended applications to Lipschitzian stability. In this way we derive efficient conditions ensuring the preservation of Lipschitzian and related properties for set-valued mappings under various operations, with the exact bound/modulus estimates, as well as new sufficient conditions for the Lipschitz continuity of marginal functions.
Robust Lipschitzian properties of set-valued mappings and marginal functions play a crucial role in many aspects of variational analysis and its applications, especially for issues related to variational stability and optimization. We develop an approach to variational stability based on generalized differentiation. The principal achievements of this paper include new results on coderivative calculus for set-valued mappings and singular subdifferentials of marginal functions in infinite dimensions with their extended applications to Lipschitzian stability. In this way we derive efficient conditions ensuring the preservation of Lipschitzian and related properties for set-valued mappings under various operations, with the exact bound/modulus estimates, as well as new sufficient conditions for the Lipschitz continuity of marginal functions. [PUBLICATION ABSTRACT]
Audience Academic
Author Mordukhovich, Boris S
Nam, Nguyen Mau
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Snippet Robust Lipschitzian properties of set-valued mappings and marginal functions play a crucial role in many aspects of variational analysis and its applications,...
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SubjectTerms Analysis
Banach space
Calculus
Chain rule
Differential calculus
Differential equations
generalized differentiation
Lipschitz condition
marginal and value functions
Mathematical analysis
Mathematical differentiation
Mathematical functions
Mathematical theorems
Operations research
Optimization
optimization and variational analysis
Property composition
robust stability and sensitivity
Sensitivity analysis
Studies
Title Variational Stability and Marginal Functions via Generalized Differentiation
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