Optimization and equilibrium problems with equilibrium constraints in infinite-dimensional spaces

The article is devoted to applications of modern variational analysis to the study of constrained optimization and equilibrium problems in infinite-dimensional spaces. We pay a particular attention to the remarkable classes of optimization and equilibrium problems identified as mathematical programs...

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Bibliographic Details
Published in:Optimization Vol. 57; no. 5; pp. 715 - 741
Main Author: Mordukhovich, Boris S.
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis Group 01.01.2008
Taylor & Francis LLC
Subjects:
Calculus of variations
Comparative analysis
Equilibrium
equilibrium constraints
generalized differentiation
infinite-dimensional spaces
Mathematical programming
necessary optimality conditions
non-smooth and multiobjective optimization
Optimization
Primary: 49J52
Secondary: 90C29
Studies
variational analysis
ISSN:0233-1934, 1029-4945
Online Access:Get full text
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Summary:The article is devoted to applications of modern variational analysis to the study of constrained optimization and equilibrium problems in infinite-dimensional spaces. We pay a particular attention to the remarkable classes of optimization and equilibrium problems identified as mathematical programs with equilibrium constraints (MPECs) and equilibrium problems with equilibrium constraints (EPECs) treated from the viewpoint of multiobjective optimization. Their underlying feature is that the major constraints are governed by parametric generalized equations/variational conditions in the sense of Robinson. Such problems are intrinsically non-smooth and can be handled by using an appropriate machinery of generalized differentiation exhibiting a rich/full calculus. The case of infinite-dimensional spaces is significantly more involved in comparison with finite dimensions, requiring in addition a certain sufficient amount of compactness and an efficient calculus of the corresponding 'sequential normal compactness' (SNC) properties.
Bibliography:SourceType-Scholarly Journals-1
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331930802355390