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Calculus Without Derivatives
Taschenbuch von Jean-Paul Penot
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.
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 is an Emeritus Professor at Université Paris 6. He has taught in Paris, Pau and Canada.
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: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Graduate Texts in Mathematics
Inhalt: xx
524 S.
ISBN-13: 9781489989420
ISBN-10: 1489989420
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Penot, Jean-Paul
Hersteller: Springer New York
Springer US, New York, N.Y.
Graduate Texts in Mathematics
Maße: 235 x 155 x 30 mm
Von/Mit: Jean-Paul Penot
Erscheinungsdatum: 13.12.2014
Gewicht: 0,814 kg
Artikel-ID: 105360939
Über den Autor
Jean-Paul Penot is an Emeritus Professor at Université Paris 6. He has taught in Paris, Pau and Canada.
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: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Graduate Texts in Mathematics
Inhalt: xx
524 S.
ISBN-13: 9781489989420
ISBN-10: 1489989420
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Penot, Jean-Paul
Hersteller: Springer New York
Springer US, New York, N.Y.
Graduate Texts in Mathematics
Maße: 235 x 155 x 30 mm
Von/Mit: Jean-Paul Penot
Erscheinungsdatum: 13.12.2014
Gewicht: 0,814 kg
Artikel-ID: 105360939
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