Calculus Without Derivatives [electronic resource] /by Jean-Paul Penot.
by Penot, Jean-Paul [author.]; SpringerLink (Online service).
Material type:
BookSeries: Graduate Texts in Mathematics: 266Publisher: New York, NY : Springer New York : 2013.Description: XX, 524 p. online resource.ISBN: 9781461445388.Subject(s): Mathematics | Global analysis (Mathematics) | Functional analysis | Systems theory | Mathematical optimization | Mathematics | Analysis | Real Functions | Optimization | Systems Theory, Control | Functional Analysis | Applications of MathematicsDDC classification: 515 Online resources: Click here to access online | Item type | Current location | Call number | Status | Date due | Barcode |
|---|---|---|---|---|---|
| MAIN LIBRARY | QA299.6-433 (Browse shelf) | Available |
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Preface -- 1 Metric and Topological Tools -- 2 Elements of Differential Calculus -- 3 Elements of Convex Analysis -- 4 Elementary and Viscosity Subdifferentials -- 5 Circa-Subdifferentials, Clarke Subdifferentials -- 6 Limiting Subdifferentials -- 7 Graded Subdifferentials, Ioffe Subdifferentials -- References -- Index .
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.
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