
Implicit Functions and Solution Mappings
A View from Variational Analysis
Springer (Publisher)
2nd Edition
Published on 18. June 2014
Book
Hardback
XXVIII, 466 pages
978-1-4939-1036-6 (ISBN)
Description
The implicit function theorem is one of the most important theorems in analysis and its many variants are basic tools in partial differential equations and numerical analysis.
This second edition of Implicit Functions and Solution Mappings presents an updated and more complete picture of the field by including solutions of problems that have been solved since the first edition was published, and places old and new results in a broader perspective. The purpose of this self-contained work is to provide a reference on the topic and to provide a unified collection of a number of results which are currently scattered throughout the literature. Updates to this edition include new sections in almost all chapters, new exercises and examples, updated commentaries to chapters and an enlarged index and references section.
This second edition of Implicit Functions and Solution Mappings presents an updated and more complete picture of the field by including solutions of problems that have been solved since the first edition was published, and places old and new results in a broader perspective. The purpose of this self-contained work is to provide a reference on the topic and to provide a unified collection of a number of results which are currently scattered throughout the literature. Updates to this edition include new sections in almost all chapters, new exercises and examples, updated commentaries to chapters and an enlarged index and references section.
Reviews / Votes
From reviews of the first edition: "The book commences with a helpful context-setting preface followed by six chapters. Each chapter starts with a useful preamble and concludes with a careful and instructive commentary, while a good set of references, a notation guide and a somewhat brief index complete this study. ... I unreservedly recommended this book to all practitioners and graduate students interested in modern optimization theory or control theory or to those just engaged by beautiful analysis cleanly described." (Jonathan Michael Browein, IEEE Control Systems Magazine, February, 2012). "This book is devoted to the theory of inverse and implicit functions and some of its modifications for solution mappings in variational problems. ... The book is targeted to a broad audience of researchers, teachers and graduate students. It can be used as well as a textbook as a reference book on the topic. Undoubtedly, it will be used by mathematicians dealing with functional and numerical analysis, optimization, adjacent branches and also by specialists in mechanics, physics, engineering, economics and so on." (Peter Zabreiko, Zentralblatt MATH, Vol. 1178, 2010). "The present monograph will be a most welcome and valuable addition. ... This book will save much time and effort, both for those doing research in variational analysis and for students learning the field. This important contribution fills a gap in the existing literature." (Stephen M. Robinson, Mathematical Reviews, Issue 2010).More details
Product info
HC runder Rücken kaschiert
Series
Language
English
Place of publication
New York, NY
United States
Target group
Upper undergraduate
Edition type
Revised edition
Illustrations
13 s/w Abbildungen, 1 farbige Abbildung
13 black & white illustrations, 1 colour illustrations, biography
Dimensions
Height: 244 mm
Width: 159 mm
Thickness: 35 mm
Weight
897 gr
ISBN-13
978-1-4939-1036-6 (9781493910366)
DOI
10.1007/978-1-4939-1037-3
Schweitzer Classification
Other editions
Additional editions

Asen L. Dontchev | R. Tyrrell Rockafellar
Implicit Functions and Solution Mappings
A View from Variational Analysis
Book
09/2016
2nd Edition
Springer
€69.54
Shipment within 15-20 days

Asen L. Dontchev | R. Tyrrell Rockafellar
Implicit Functions and Solution Mappings
A View from Variational Analysis
E-Book
06/2014
2nd Edition
Springer
€69.54
Available for download
Previous edition

Assen L. Dontchev | R. Tyrrell Rockafellar
Implicit Functions and Solution Mappings
A View from Variational Analysis
Book
06/2009
Springer
€64.15
Article exhausted; check for reprint
Persons
Asen L. Dontchev is a Professor at the Department of Mathematics at the University of Michigan. R. Tyrrell Rockafellar is a Professor at the Department of Mathematics at the University of Washington and at the Department of Industrial and Systems Engineering at the University of Florida.
Content
Introduction and equation-solving background.- Solution mappings for variational problems.- Set-valued analysis of solution mappings.- Regularity properties through generalized derivatives.- Metric regularity in infinite dimensions.- Applications in numerical variational analysis.