Overview
- 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
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Monographs in Mathematics (SMM)
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Table of contents (9 chapters)
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Front Matter
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Back Matter
Keywords
- metric regularity error bound
- perturbation stability analysis
- perturbation theory stability
- set-valued mappings generalized equations
- variational inequalities over polyhedral sets
- mappings with special structures
- necessary optimality conditions
- necessary optimality conditions in constraint
- metric fixed point theory
- distance metric theory
- regularity theory math
- alternating projections for convex sets
- alternating projections for nonconvex sets
- non-differentiable functions curves of descent
- calculus of subdifferentials
- calculus of coderivatives
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
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)
Authors and Affiliations
Bibliographic Information
Book Title: Variational Analysis of Regular Mappings
Book Subtitle: Theory and Applications
Authors: Alexander D. Ioffe
Series Title: Springer Monographs in Mathematics
DOI: https://doi.org/10.1007/978-3-319-64277-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-64276-5Published: 09 November 2017
Softcover ISBN: 978-3-319-87761-7Published: 24 August 2018
eBook ISBN: 978-3-319-64277-2Published: 26 October 2017
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 1
Number of Pages: XXI, 495
Number of Illustrations: 9 b/w illustrations, 2 illustrations in colour
Topics: Calculus of Variations and Optimal Control; Optimization, Continuous Optimization, Functional Analysis, Global Analysis and Analysis on Manifolds, Difference and Functional Equations