Springer Monographs in Mathematics

Variational Analysis and Applications

Authors: Mordukhovich, Boris S.

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  • Presents applications focusing on new classes of variational problems and models from economics, applied sciences, and engineering
  • Comprehensive commentaries emphasize the essence of major results, track the genesis of ideas, provide historical comments, and illuminate challenging open questions and directions for future research
  • Large number of exercises help readers better understand the basic material and develop research skills
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  • ISBN 978-3-319-92775-6
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Hardcover $149.99
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  • ISBN 978-3-319-92773-2
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  • Usually dispatched within 3 to 5 business days.
About this book

Building on fundamental results in variational analysis, this monograph presents new and recent developments in the field as well as selected applications. Accessible to a broad spectrum of potential readers, the main material is presented in finite-dimensional spaces. Infinite-dimensional developments are discussed at the end of each chapter with comprehensive commentaries which emphasize the essence of major results, track the genesis of ideas, provide historical comments, and illuminate challenging open questions and directions for future research.

The first half of the book (Chapters 1–6) gives a systematic exposition of key concepts and facts, containing basic material as well as some recent and new developments. These first chapters are particularly accessible to masters/doctoral students taking courses in modern optimization, variational analysis, applied analysis, variational inequalities, and variational methods. The reader’s development of skills will be facilitated as they work through each, or a portion of, the multitude of exercises of varying levels. Additionally, the reader may find hints and references to more difficult exercises and are encouraged to receive further inspiration from the gems in chapter commentaries. Chapters 7–10 focus on recent results and applications of variational analysis to advanced problems in modern optimization theory, including its hierarchical and multiobjective aspects, as well as microeconomics, and related areas. It will be of great use to researchers and professionals in applied and behavioral sciences and engineering.

About the authors

Boris S. Mordukhovich is a Distinguished University Professor of Mathematics at Wayne State University. His areas of research include optimization and variational analysis, control theory, nonlinear systems, generalized differentiation, and various applications. Professor Mordukhovich has authored more than 400 publications including two volumes in Springer’s Grundlehren series entitled “Variational Analysis and Generalized Differentiation.” He is a Fellow of the American Mathematical Society (AMS) and the Society of Industrial and Applied Mathematics (SIAM).

Reviews

“Written by an expert in the areas of variational analysis and optimization and based on his didactic experience, this is an excellent textbook. By the wealth of information contained in the second part of the book and in exercises, it can be also used by researchers in optimization theory and its applications as a reference text.” (S. Cobzaş, Studia Universitatis Babes-Bolyai Mathematica, Vol. 6 (04). 2018)

Table of contents (10 chapters)

  • Constructions of Generalized Differentiation

    Mordukhovich, Boris S.

    Pages 1-66

  • Fundamental Principles of Variational Analysis

    Mordukhovich, Boris S.

    Pages 67-102

  • Well-Posedness and Coderivative Calculus

    Mordukhovich, Boris S.

    Pages 103-160

  • First-Order Subdifferential Calculus

    Mordukhovich, Boris S.

    Pages 161-190

  • Coderivatives of Maximal Monotone Operators

    Mordukhovich, Boris S.

    Pages 191-218

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-3-319-92775-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.99
price for USA in USD
  • ISBN 978-3-319-92773-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Variational Analysis and Applications
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG, part of Springer Nature
eBook ISBN
978-3-319-92775-6
DOI
10.1007/978-3-319-92775-6
Hardcover ISBN
978-3-319-92773-2
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XIX, 622
Number of Illustrations
36 illustrations in colour
Topics