Nonsmooth Analysis

2007
ISBN: 978-3-540-71332-6
Verlag: Springer Berlin Heidelberg

Buch, Englisch, 378 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 593 g

Reihe: Universitext

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Schirotzek, Winfried

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe
• Technische Wissenschaften Elektronik | Nachrichtentechnik Elektronik Überwachungstechnik

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.