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METRIC REGULARITY—A SURVEY PART II. APPLICATIONS

Part of: Calculus on manifolds; nonlinear operators Existence theories Nonlinear operators and their properties Maps and general types of spaces defined by maps Optimality conditions Topological linear spaces and related structures

Published online by Cambridge University Press:  08 July 2016

A. D. IOFFE
A. D. IOFFE*
Affiliation:
Department of Mathematics, Technion, Haifa 32000, Israel email ioffe@tx.technion.ac.il
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Abstract

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Metric regularity theory lies in the very heart of variational analysis, a relatively new discipline whose appearance was, to a large extent, determined by the needs of modern optimization theory in which such phenomena as nondifferentiability and set-valued mappings naturally appear. The roots of the theory go back to such fundamental results of the classical analysis as the implicit function theorem, Sard theorem and some others. The paper offers a survey of the state of the art of some principal parts of the theory along with a variety of its applications in analysis and optimization.

Keywords

set-valued mappingregularitytransversalityimplicit functionLipschitz stabilitySard theorem

MSC classification

Primary: 49J53: Set-valued and variational analysis
Secondary: 54C60: Set-valued maps 58C06: Set valued and function-space valued mappings 47H04: Set-valued operators 49K40: Sensitivity, stability, well-posedness 46A30: Open mapping and closed graph theorems; completeness (including $B$-, $B_r$-completeness) 90C31: Sensitivity, stability, parametric optimization
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 101 , Issue 3 , December 2016 , pp. 376 - 417
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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