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 Uspekhi Mat. Nauk, 2000, Volume 55, Issue 3(333), Pages 103–162 (Mi umn292)

Metric regularity and subdifferential calculus

A. D. Ioffe

Technion – Israel Institute of Technology

Abstract: The theory of metric regularity is an extension of two classical results: the Lyusternik tangent space theorem and the Graves surjection theorem. Developments in non-smooth analysis in the 1980s and 1990s paved the way for a number of far-reaching extensions of these results. It was also well understood that the phenomena behind the results are of metric origin, not connected with any linear structure. At the same time it became clear that some basic hypotheses of the subdifferential calculus are closely connected with the metric regularity of certain set-valued maps. The survey is devoted to the metric theory of metric regularity and its connection with subdifferential calculus in Banach spaces.

DOI: https://doi.org/10.4213/rm292

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English version:
Russian Mathematical Surveys, 2000, 55:3, 501–558

Bibliographic databases:

UDC: 517
MSC: Primary 49J52, 58C20; Secondary 58C06, 58E05, 49J53, 46G05, 46A30, 54C60, 49J50

Citation: A. D. Ioffe, “Metric regularity and subdifferential calculus”, Uspekhi Mat. Nauk, 55:3(333) (2000), 103–162; Russian Math. Surveys, 55:3 (2000), 501–558

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