Springer Monographs in Mathematics

Variational Analysis of Regular Mappings

Theory and Applications

Authors: Ioffe, Alexander

  • Presents a detailed study of regularity properties of mappings in metric spaces
  • Covers mappings with specific structures in Banach and finite dimensional spaces
  • Offers new and previously unrecorded applications of regularity theory
  • Emphasizes the quantitative character of regularity theory
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eBook $109.00
price for USA in USD (gross)
  • ISBN 978-3-319-64277-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-3-319-64276-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

This monograph offers the first systematic account of (metric) regularity theory in variational analysis. It presents new developments alongside classical results and demonstrates the power of the theory through applications to various problems in analysis and optimization theory.

The origins of metric regularity theory can be traced back to a series of fundamental ideas and results of nonlinear functional analysis and global analysis centered around problems of existence and stability of solutions of nonlinear equations. In variational analysis, regularity theory goes far beyond the classical setting and is also concerned with non-differentiable and multi-valued operators. The present volume explores all basic aspects of the theory, from the most general problems for mappings between metric spaces to those connected with fairly concrete and important classes of operators acting in Banach and finite dimensional spaces. Written by a leading expert in the field, the book covers new and powerful techniques, which have proven to be highly efficient even in classical settings, and outlines the theory’s predominantly quantitative character, leading to a variety of new and unexpected applications.

Variational Analysis of Regular Mappings is aimed at graduate students and researchers in nonlinear and functional analysis, especially those working in areas close to optimization and optimal control, and will be suitable to anyone interested in applying new concepts and ideas to operations research, control engineering and numerical analysis.

Reviews

“The book is an excellent extensive contribution to the theory of metric regularity and its
role in analysis and optimization. ... The book is a research monograph offering an extensive presentation of the main developments in the field. Its audience includes graduate students and researchers in the field.” (Gheorghe Moroșanu, zbMATH 1381.49001, 2018)

Table of contents (9 chapters)

  • The Classical Theory

    Ioffe, Alexander D.

    Pages 1-31

  • Metric Theory: Phenomenology

    Ioffe, Alexander D.

    Pages 33-97

  • Metric Theory: The Infinitesimal Viewpoint

    Ioffe, Alexander D.

    Pages 99-140

  • Subdifferentials: A Short Introduction

    Ioffe, Alexander D.

    Pages 141-193

  • Banach Space Theory: Regularity Criteria

    Ioffe, Alexander D.

    Pages 195-243

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-3-319-64277-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-3-319-64276-5
  • 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 of Regular Mappings
Book Subtitle
Theory and Applications
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-64277-2
DOI
10.1007/978-3-319-64277-2
Hardcover ISBN
978-3-319-64276-5
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XXI, 495
Number of Illustrations and Tables
9 b/w illustrations, 2 illustrations in colour
Topics