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Cover: 9783540713326 | Nonsmooth Analysis | Winfried Schirotzek | Taschenbuch | Universitext
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Nonsmooth Analysis
Taschenbuch von Winfried Schirotzek
Sprache: Englisch

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Beschreibung
This book treats various concepts of generalized derivatives and subdifferentials in normed spaces, their geometric counterparts and their application to optimization problems. It starts with the subdifferential of convex analysis, passes to corresponding concepts for locally Lipschitz continuous functions and then presents subdifferentials for general lower semicontinuous functions. All basic tools are presented where they are needed: this concerns separation theorems, variational and extremal principles as well as relevant parts of multifunction theory. Each chapter ends with bibliographic notes and exercises.
This book treats various concepts of generalized derivatives and subdifferentials in normed spaces, their geometric counterparts and their application to optimization problems. It starts with the subdifferential of convex analysis, passes to corresponding concepts for locally Lipschitz continuous functions and then presents subdifferentials for general lower semicontinuous functions. All basic tools are presented where they are needed: this concerns separation theorems, variational and extremal principles as well as relevant parts of multifunction theory. Each chapter ends with bibliographic notes and exercises.
Zusammenfassung

This book treats various concepts of generalized derivatives and subdifferentials in normed spaces, their geometric counterparts (tangent and normal cones) and their application to optimization problems. It starts with the subdifferential of convex analysis, passes to corresponding concepts for locally Lipschitz continuous functions and then presents subdifferentials for general lower semicontinuous functions. All basic tools are presented where they are needed: this concerns separation theorems, variational and extremal principles as well as relevant parts of multifunction theory. The presentation is rigorous, with detailed proofs. Each chapter ends with bibliographic notes and exercises.

Inhaltsverzeichnis
Preliminaries.- The Conjugate of Convex Functionals.- Classical Derivatives.- The Subdifferential of Convex Functionals.- Optimality Conditions for Convex Problems.- Duality of Convex Problems.- Derivatives and Subdifferentials of Lipschitz Functionals.- Variational Principles.- Subdifferentials of Lower Semicontinuous Functionals.- Multifunctions.- Tangent and Normal Cones.- Optimality Conditions for Nonconvex Problems.- Extremal Principles and More Normals and Subdifferentials.
Details
Erscheinungsjahr: 2007
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Universitext
Inhalt: xii
378 S.
31 s/w Illustr.
378 p. 31 illus.
ISBN-13: 9783540713326
ISBN-10: 3540713328
Sprache: Englisch
Herstellernummer: 12029495
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Schirotzek, Winfried
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Universitext
Maße: 235 x 155 x 22 mm
Von/Mit: Winfried Schirotzek
Erscheinungsdatum: 11.06.2007
Gewicht: 0,593 kg
Artikel-ID: 102066141
Zusammenfassung

This book treats various concepts of generalized derivatives and subdifferentials in normed spaces, their geometric counterparts (tangent and normal cones) and their application to optimization problems. It starts with the subdifferential of convex analysis, passes to corresponding concepts for locally Lipschitz continuous functions and then presents subdifferentials for general lower semicontinuous functions. All basic tools are presented where they are needed: this concerns separation theorems, variational and extremal principles as well as relevant parts of multifunction theory. The presentation is rigorous, with detailed proofs. Each chapter ends with bibliographic notes and exercises.

Inhaltsverzeichnis
Preliminaries.- The Conjugate of Convex Functionals.- Classical Derivatives.- The Subdifferential of Convex Functionals.- Optimality Conditions for Convex Problems.- Duality of Convex Problems.- Derivatives and Subdifferentials of Lipschitz Functionals.- Variational Principles.- Subdifferentials of Lower Semicontinuous Functionals.- Multifunctions.- Tangent and Normal Cones.- Optimality Conditions for Nonconvex Problems.- Extremal Principles and More Normals and Subdifferentials.
Details
Erscheinungsjahr: 2007
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Universitext
Inhalt: xii
378 S.
31 s/w Illustr.
378 p. 31 illus.
ISBN-13: 9783540713326
ISBN-10: 3540713328
Sprache: Englisch
Herstellernummer: 12029495
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Schirotzek, Winfried
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Universitext
Maße: 235 x 155 x 22 mm
Von/Mit: Winfried Schirotzek
Erscheinungsdatum: 11.06.2007
Gewicht: 0,593 kg
Artikel-ID: 102066141
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