Calculus Without Derivatives

Calculus Without Derivatives expounds the foundations and recent advances in nonsmooth analysis, a powerful compound of mathematical tools that obviates the usual smoothness assumptions. This textbook also provides significant tools and methods towards applications, in particular optimization problems. Whereas most books on this subject focus on a particular theory, this text takes a general approach including all main theories.

In order to be self-contained, the book includes three chapters of preliminary material, each of which can be used as an independent course if needed. The first chapter deals with metric properties, variational principles, decrease principles, methods of error bounds, calmness and metric regularity. The second one presents the classical tools of differential calculus and includes a section about the calculus of variations. The third contains a clear exposition of convex analysis.

Table of Contents

Chapter 1 Metric and Topological Tools

Chapter 2 Elements of Differential Calculus

Chapter 3 Elements of Convex Analysis

Chapter 4 Elementary and Viscosity Subdifferentials

Chapter 5 Circa-Subdifferentials, Clarke Subdifferentials

Chapter 6 Limiting Subdifferentials

Chapter 7 Graded Subdifferentials, loffe Subdifferentials

About the Author

Jean-Paul Penot is an Emeritus Professor at Université Paris 6. He has taught in Paris, Pau and Canada.