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Nonsmooth Analysis and Control Theory : Graduate Texts in Mathematics - F.H. Clarke

Nonsmooth Analysis and Control Theory

Graduate Texts in Mathematics

Hardcover Published: 1st January 1998
ISBN: 9780387983363
Number Of Pages: 278

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In the last decades the subject of nonsmooth analysis has grown rapidly due to the recognition that nondifferentiable phenomena are more widespread, and play a more important role, than had been thought. In recent years, it has come to play a role in functional analysis, optimization, optimal design, mechanics and plasticity, differential equations, control theory, and, increasingly, in analysis. This volume presents the essentials of the subject clearly and succinctly, together with some of its applications and a generous supply of interesting exercises. The book begins with an introductory chapter which gives the reader a sampling of what is to come while indicating at an early stage why the subject is of interest. The next three chapters constitute a course in nonsmooth analysis and identify a coherent and comprehensive approach to the subject leading to an efficient, natural, yet powerful body of theory. The last chapter, as its name implies, is a self-contained introduction to the theory of control of ordinary differential equations. End-of-chapter problems also offer scope for deeper understanding. The authors have incorporated in the text a number of new results which clarify the relationships between the different schools of thought in the subject. Their goal is to make nonsmooth analysis accessible to a wider audience. In this spirit, the book is written so as to be used by anyone who has taken a course in functional analysis.

Preface
List of Figures
Introductionp. 1
Proximal Calculus in Hilbert Spacep. 21
Generalized Gradients in Banach Spacep. 69
Special Topicsp. 103
A Short Course in Control Theoryp. 177
Notes and Commentsp. 257
List of Notationp. 263
Bibliographyp. 265
Indexp. 273
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780387983363
ISBN-10: 0387983368
Series: Graduate Texts in Mathematics
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 278
Published: 1st January 1998
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 24.13 x 16.13  x 2.11
Weight (kg): 0.59