Techniques in Variational Analysis

Jonathan M. Borwein, Qiji Zhu9780387242989, 0-387-24298-8

Variational arguments are classical techniques whose use can be traced back to the early development of the calculus of variations and further. Rooted in the physical principle of least action, they have wide applications in diverse fields. This book provides a concise account of the essential tools of infinite-dimensional first-order variational analysis. These tools are illustrated by applications in many different parts of analysis, optimization and approximation, dynamical systems, mathematical economics and elsewhere. Much of the material in the book grows out of talks and short lecture series given by the authors in the past several years. Thus, chapters in this book can easily be arranged to form material for a graduate level topics course. A sizeable collection of suitable exercises is provided for this purpose. In addition, this book is also a useful reference for researchers who use variational techniques – or just think they might like to.

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Table of contents :
front-matter……Page 1
1Introduction and Notation……Page 10
2Variational Principles……Page 14
3Variational Techniques in Subdifferential Theory……Page 46
4Variational Techniques in Convex Analysis……Page 119
5Variational Techniques and Multifunctions……Page 172
6Variational Principles in Nonlinear Functional Analysis……Page 249
7Variational Techniques In the Presence of Symmetry……Page 296
back-matter……Page 344