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Journal of Convex Analysis 15 (2008), No. 2, 365--380
Copyright Heldermann Verlag 2008

Characterization of Metric Regularity of Subdifferentials

Francisco Javier Aragón Artacho
Dept. of Statistics and Operations Research, University of Alicante, 03071 Alicante, Spain

Michel H. Geoffroy
Laboratoire AOC, Dép. de Mathématiques, Université Antilles-Guyane, 97159 Pointe-à-Pitre, Guadeloupe -- France

We study regularity properties of the subdifferential of proper lower semicontinuous convex functions in Hilbert spaces. More precisely, we investigate the metric regularity and subregularity, the strong regularity and subregularity of such a subdifferential. We characterize each of these properties in terms of a growth condition involving the function.

Keywords: Set-valued mapping, subdifferential, metric regularity, quadratic growth condition.

MSC: 49J52, 49J53

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