First-order and second-order optimality conditions for nonsmooth constrained problems via convolution smoothing

This article mainly concerns deriving first-order and second-order necessary (and partly sufficient) optimality conditions for a general class of constrained optimization problems via smoothing regularization procedures based on infimal-like convolutions/envelopes. In this way, we obtain first-order...

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Vydáno v:Optimization Ročník 60; číslo 1-2; s. 253 - 275
Hlavní autoři: Eberhard, Andrew C., Mordukhovich, Boris S.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia Taylor & Francis Group 01.01.2011
Taylor & Francis LLC
Témata:
constrained optimization
Constraints
Construction
Convolution
Derivatives
Differential equations
Envelopes
first-order and second-order optimality conditions
generalized differentiation
Mathematical problems
Optimization
Optimization algorithms
Regularization
Smoothing
Studies
variational analysis
ISSN:0233-1934, 1029-4945
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Abstract This article mainly concerns deriving first-order and second-order necessary (and partly sufficient) optimality conditions for a general class of constrained optimization problems via smoothing regularization procedures based on infimal-like convolutions/envelopes. In this way, we obtain first-order optimality conditions of both lower subdifferential and upper subdifferential types and then second-order conditions of three kinds involving, respectively, generalized second-order directional derivatives, graphical derivatives of first-order subdifferentials and second-order subdifferentials defined via coderivatives of first-order constructions.
AbstractList This article mainly concerns deriving first-order and second-order necessary (and partly sufficient) optimality conditions for a general class of constrained optimization problems via smoothing regularization procedures based on infimal-like convolutions/envelopes. In this way, we obtain first-order optimality conditions of both lower subdifferential and upper subdifferential types and then second-order conditions of three kinds involving, respectively, generalized second-order directional derivatives, graphical derivatives of first-order subdifferentials and second-order subdifferentials defined via coderivatives of first-order constructions. [PUBLICATION ABSTRACT]
This article mainly concerns deriving first-order and second-order necessary (and partly sufficient) optimality conditions for a general class of constrained optimization problems via smoothing regularization procedures based on infimal-like convolutions/envelopes. In this way, we obtain first-order optimality conditions of both lower subdifferential and upper subdifferential types and then second-order conditions of three kinds involving, respectively, generalized second-order directional derivatives, graphical derivatives of first-order subdifferentials and second-order subdifferentials defined via coderivatives of first-order constructions.
Author Eberhard, Andrew C.
Mordukhovich, Boris S.
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  email: boris@math.wayne.edu.
  organization: Department of Mathematics , Wayne State University
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StartPage 253
SubjectTerms constrained optimization
Constraints
Construction
Convolution
Derivatives
Differential equations
Envelopes
first-order and second-order optimality conditions
generalized differentiation
Mathematical problems
Optimization
Optimization algorithms
Regularization
Smoothing
Studies
variational analysis
Title First-order and second-order optimality conditions for nonsmooth constrained problems via convolution smoothing
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