Nonsmooth Analysis

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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.



The reader is required to have a basic knowledge of functional analysis only. All further prerequisites are presented in the book

The presentation strictly proceeds from simple to more difficult

The presentation is rigorous, with detailed proofs. Each chapter ends with suggestions for further study and with exercises

Includes supplementary material: sn.pub/extras



Inhalt
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.

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Produktinformationen

Titel
Nonsmooth Analysis
Autor
EAN
9783540713326
ISBN
978-3-540-71332-6
Format
Kartonierter Einband
Herausgeber
Springer, Berlin
Genre
Mathematik
Anzahl Seiten
378
Gewicht
606g
Größe
H22mm x B236mm x T156mm
Jahr
2007
Untertitel
Englisch
Auflage
2007
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