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Variational analysis of regular mappings : theory and applications

Author: Aleksandr Davidovich Ioffe
Publisher: Cham, Switzerland : Springer, [2017] ©2017
Series: Springer monographs in mathematics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Ioffe, Alexander D.
Variational analysis of regular mappings.
Cham, Switzerland : Springer, [2017]
(OCoLC)992747098
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Aleksandr Davidovich Ioffe
ISBN: 9783319642772 3319642774
OCLC Number: 1008868228
Description: 1 online resource.
Contents: 1 The Classical Theory --
2 Metric Theory: Phenomenology --
3 Metric Theory: The Infinitesimal Viewpoint --
4 Subdifferentials: A Short Introduction --
5 Banach Space Theory: Regularity Criteria --
6 Banach Space Theory: Special Classes of Mappings --
7 Applications to Analysis and Optimization 1 --
8 Regularity in Finite-Dimensional Spaces --
9 Applications to Analysis and Optimization 2.
Series Title: Springer monographs in mathematics.
Responsibility: Alexander D. Ioffe.

Abstract:

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.--

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"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 Read more...

 
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