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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Bibliographic Details
Published in:Optimization Vol. 60; no. 1-2; pp. 253 - 275
Main Authors: Eberhard, Andrew C., Mordukhovich, Boris S.
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis Group 01.01.2011
Taylor & Francis LLC
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2010.522713