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The Resource Implicit Functions and Solution Mappings : A View from Variational Analysis, by Asen L. Dontchev, R. Tyrrell Rockafellar, (electronic resource)

Implicit Functions and Solution Mappings : A View from Variational Analysis, by Asen L. Dontchev, R. Tyrrell Rockafellar, (electronic resource)

Creator
Author
Contributor
Summary
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. 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)
Language
eng
Work
Publication
Edition
Second edition 2014.
Extent
XXVIII, 466 pages 14 illustrations, 1 illustrations in color.
Contents
  • 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
Isbn
9781493910373
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-1-4939-1037-3
Instance
Label
Implicit Functions and Solution Mappings : A View from Variational Analysis
Title
Implicit Functions and Solution Mappings
Title remainder
A View from Variational Analysis
Statement of responsibility
by Asen L. Dontchev, R. Tyrrell Rockafellar
Creator
Contributor
Author
Subject
Language
eng
Summary
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. 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)
Member of
Cataloging source
IT-FiEUI
http://library.link/vocab/creatorName
Dontchev, Asen L
Image bit depth
0
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorDate
1935-.
http://library.link/vocab/relatedWorkOrContributorName
  • Rockafellar, R. Tyrrell
  • SpringerLink (Online service)
Series statement
  • Springer Series in Operations Research and Financial Engineering,
  • Springer eBooks
http://library.link/vocab/subjectName
  • Mathematics
  • Global analysis (Mathematics)
  • Numerical analysis
  • Mathematical optimization
Label
Implicit Functions and Solution Mappings : A View from Variational Analysis, by Asen L. Dontchev, R. Tyrrell Rockafellar, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-1-4939-1037-3
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
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
Control code
978-1-4939-1037-3
Dimensions
unknown
Edition
Second edition 2014.
Extent
XXVIII, 466 pages 14 illustrations, 1 illustrations in color.
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9781493910373
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-1-4939-1037-3
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1086457926
Label
Implicit Functions and Solution Mappings : A View from Variational Analysis, by Asen L. Dontchev, R. Tyrrell Rockafellar, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-1-4939-1037-3
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
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
Control code
978-1-4939-1037-3
Dimensions
unknown
Edition
Second edition 2014.
Extent
XXVIII, 466 pages 14 illustrations, 1 illustrations in color.
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9781493910373
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-1-4939-1037-3
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1086457926

Subject

Member of

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