The 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 finally 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.
Author(s): Winfried Schirotzek
Series: Universitext
Edition: 1
Publisher: Springer
Year: 2007
Language: English
Pages: 380
Cover......Page 1
Preface......Page 6
Table of Contents......Page 7
Introduction......Page 11
1 Preliminaries......Page 15
2 The Conjugate of Convex Functionals......Page 36
3 Classical Derivatives......Page 48
4 The Subdifferential of Convex Functionals......Page 68
5 Optimality Conditions for Convex Problems......Page 100
6 Duality of Convex Problems......Page 120
7 Derivatives and Subdifferentials of Lipschitz Functionals......Page 140
8 Variational Principles......Page 163
9 Subdifferentials of Lower Semicontinuous Functionals......Page 175
10 Multifunctions......Page 203
11 Tangent and Normal Cones......Page 238
12 Optimality Conditions for Nonconvex Problems......Page 271
13 Extremal Principles and More Normals and Subdifferentials......Page 291
Appendix: Further Topics......Page 352
References......Page 356
Notation......Page 367
Index......Page 370
