Variational Analysis of Regular Mappings: Theory and Applications (Springer Monographs in Mathematics) - Hardcover

Ioffe, Alexander D.

Hardcover

ISBN 10: 3319642766 ISBN 13: 9783319642765

Publisher: Springer, 2017

Synopsis

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.

About this title

From the Back Cover

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 coversnew 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.

Edition details

• Publisher: Springer
• Publication date: 2017
• Language: English
• ISBN 10: 3319642766
• ISBN 13: 9783319642765
• Binding: Hardcover
• Edition number: 1
• Number of pages: 516