Calculus without derivatives

Description

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. Front Matter....Pages i-xx Metric and Topological Tools....Pages 1-115 Elements of Differential Calculus....Pages 117-186 Elements of Convex Analysis....Pages 187-261 Elementary and Viscosity Subdifferentials....Pages 263-356 Circa-Subdifferentials, Clarke Subdifferentials....Pages 357-405 Limiting Subdifferentials....Pages 407-462 Graded Subdifferentials, Ioffe Subdifferentials....Pages 463-478 Back Matter....Pages 479-524