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METRIC REGULARITY—A SURVEY PART 1. THEORY

Part of: Miscellaneous topics in calculus of variations and optimal control

Published online by Cambridge University Press:  14 July 2016

A. D. IOFFE
A. D. IOFFE*
Affiliation:
Department of Mathematics, Technion, Haifa 32000, Israel email alexander.ioffe38@gmail.com, ioffe@tx.technion.ac.il
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Abstract

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Metric regularity theory lies at 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. This 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

metric regularityinverse function theoremserror boundsvariational analysis

MSC classification

Secondary: 49N99: None of the above, but in this section 90C26: Nonconvex programming, global optimization
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 101 , Issue 2 , October 2016 , pp. 188 - 243
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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