Fréchet subdifferential calculus and optimality conditions in nondifferentiable programming

We develop various (exact) calculus rules for Fréchet lower and upper subgradients of extended-real-valued functions in real Banach spaces. Then we apply this calculus to derive new necessary optimality conditions for some remarkable classes of problems in constrained optimization including minimiza...

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Bibliographic Details
Published in:Optimization Vol. 55; no. 5-6; pp. 685 - 708
Main Authors: Mordukhovich, B. S., Nam, N. M., Yen, N. D.
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis Group 01.10.2006
Taylor & Francis LLC
Subjects:
Calculus
Coderivatives
Difference-type functions
Fréchet normals
Geometric and operator constraints
Mathematical functions
Mathematics Subject Classifications 2000
Necessary optimality conditions
Optimization
Primary: 49J52
Secondary: 90C30
Studies
Subdifferential calculus
Subgradients
Variational analysis and constrained optimization
Weak sharp minima
ISSN:0233-1934, 1029-4945
Online Access:Get full text
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Summary:We develop various (exact) calculus rules for Fréchet lower and upper subgradients of extended-real-valued functions in real Banach spaces. Then we apply this calculus to derive new necessary optimality conditions for some remarkable classes of problems in constrained optimization including minimization problems for difference-type functions under geometric and operator constraints as well as subdifferential optimality conditions for the so-called weak sharp minima. §Dedicated to Diethard Pallaschke in honor of his 65th birthday.
Bibliography:SourceType-Scholarly Journals-1
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331930600816395