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Variational Analysis and Generalized Differentiation I
ISBN-13:
9783540312475
Veröffentl:
2006
Seiten:
579
Autor:
Boris S. Mordukhovich
Serie:
330, Grundlehren der mathematischen Wissenschaften
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
1 - PDF Watermark
Sprache:
Englisch
Beschreibung:
Variational analysis is a fruitful area in mathematics that, on the one hand, deals with the study of optimization and equilibrium problems and, on the other hand, applies optimization, perturbation, and approximation ideas to the analysis of a broad range of problems that may not be of a variational nature. One of the most characteristic features of modern variational analysis is the intrinsic presence of nonsmoothness, which enters naturally not only through initial data of optimization-related problems but largely via variational principles and perturbation techniques. Thus generalized differential lies at the heart of variational analysis and its applications.
"Variational analysis is a fruitful area in mathematics that, on one hand, deals with the study of optimization and equilibrium problems and, on the other hand, applies optimization, perturbation, and approximation ideas to the analysis of a broad range of problems that may not be of a variational nature.
Generalized Differentiation in Banach Spaces: Generalized Normals to Nonconvex Sets. Coderivatives of Set-Valued Mappings. Subdifferentials of Nonsmooth Functions.- Extremal Principle in Variational Analysis: Set Extremality and Nonconvex Separation. Extremal Principle in Asplund Spaces. Relations with Variational Principles. Representations and Characterizations in Asplund Spaces. Versions of the Extremal Principle in Banach Spaces.- Full Calculus in Asplund Spaces: Calculus Rules for Normals and Coderivatives. Subdifferential Calculus and Related Topics. SNC Calculus for Sets and Mappings.- Lipschitzian Stability and Sensivity Analysis: Neighborhood Criteria and Exact Bounds. Pointbased Characterizations. Sensitivity Analysis for Constraint Systems. Sensitivity Analysis for Variational Systems.- References.- Glossary of Notation.- Index of Statements.
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