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Implicit functions and solution mappings. Dontchev, R. Tyrrell Rockafellar : a view from variational analysis

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 book treats the implicit function paradigm in the classical framework and beyond, focusing largely on properties of solution mappings of variational problems. 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. The first chapter of the book treats the classical implicit function theorem in a way that will be useful for students and teachers of undergraduate calculus. The remaining part becomes gradually more advanced, and considers implicit mappings defined by relations other than equations, e.g., variational problems. Applications to numerical analysis and optimization are also provided. This valuable book is a major achievement and is sure to become a standard reference on the topic.

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  • "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 book treats the implicit function paradigm in the classical framework and beyond, focusing largely on properties of solution mappings of variational problems. 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. The first chapter of the book treats the classical implicit function theorem in a way that will be useful for students and teachers of undergraduate calculus. The remaining part becomes gradually more advanced, and considers implicit mappings defined by relations other than equations, e.g., variational problems. Applications to numerical analysis and optimization are also provided. This valuable book is a major achievement and is sure to become a standard reference on the topic."@en
  • "This second edition ... 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.--Provided by publisher."@en
  • "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)"@en

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  • "Online-Publikation"
  • "Electronic books"@en
  • "Electronic books"

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  • "Implicit functions and solution mappings : a view from varational analysis"
  • "Implicit functions and solution mappings. Dontchev, R. Tyrrell Rockafellar : a view from variational analysis"@en
  • "Implicit Functions and Solution Mappings : A View from Variational Analysis"
  • "Implicit functions and solution mappings : a view from variational vnalysis"
  • "Implicit Functions and Solution Mappings A View from Variational Analysis"
  • "Implicit functions and solution mappings a view from variational analysis"@en
  • "Implicit functions and solution mappings a view from variational analysis"
  • "Implicit Functions and Solution Mappings a View from Variational Analysis"@en
  • "Implicit functions and solution mappings : a view from variational analysis"@en
  • "Implicit functions and solution mappings : a view from variational analysis"
  • "Implicit functions and solution mappings"

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