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METRIC REGULARITY—A SURVEY PART 1. THEORY

Published online by Cambridge University Press:  14 July 2016

A. D. IOFFE*
Affiliation:
Department of Mathematics, Technion, Haifa 32000, Israel email [email protected], [email protected]
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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.

Type
Research Article
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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