Jean-Paul Penot: Calculus Without Derivatives

Cover: 9781489989420 | Calculus Without Derivatives | Jean-Paul Penot | Taschenbuch | xx

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

Jean-Paul Penot has published about 250 research articles and two books, including Calculus Without Derivatives, Graduate Texts in Mathematics Volume 266, Springer. He has taught in Paris (France), Sherbrooke (Canada), Pau (France) and participated in numerous conferences. His research interests include global analysis, optimization, convex analysis and nonsmooth analysis.

Zusammenfassung

Includes all necessary preliminary material

Introduces fundamental aspects of nonsmooth analysis that impact many applications

Presents a balanced picture of the most elementary attempts to replace a derivative with a one-sided generalized derivative called a subdifferential

Includes references, notes, exercises and supplements that will give the reader a thorough insight into the subject

Includes supplementary material: [...]

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2014
Fachbereich:	Analysis
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Graduate Texts in Mathematics
Inhalt:	xx 524 S.
ISBN-13:	9781489989420
ISBN-10:	1489989420
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Penot, Jean-Paul
Hersteller:	Humana Springer Springer US, New York, N.Y. Graduate Texts in Mathematics
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 30 mm
Von/Mit:	Jean-Paul Penot
Erscheinungsdatum:	13.12.2014
Gewicht:	0,814 kg