Nonsmooth Analysis

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Springer Science & Business Media, May 26, 2007 - Mathematics - 378 pages
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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.

 

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Contents

Introduction
1
The Conjugate of Convex Functionals 27
26
Classical Derivatives
39
Optimality Conditions for Convex Problems
91
Duality of Convex Problems
111
Derivatives and Subdifferentials of Lipschitz Functionals
131
Variational Principles
155
Subdifferentials of Lower Semicontinuous Functionals
167
Further Topics 347
346
Notation
363
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