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Journal of Convex Analysis 08 (2001), No. 1, 197--222
Copyright Heldermann Verlag 2001



Variational Inequalities and Regularity Properties of Closed Sets in Hilbert Spaces

Giovanni Colombo
Dip. di Matematica Pura ed Applicata, UniversitÓ di Padova, Via Belzoni 7, 35131 Padova, Italy

Vladimirov V. Goncharov
Institute of System Dynamics and Control Theory, Russian Academy of Sciences, ul. Lermontov 134, 664033 Irkutsk, Russia



Some properties of closed sets which generalize concepts of Convex Analysis are compared and characterized. Some of them have a global character and are concerned with controlling the lack of monotonicity of the Frechet subdifferential of the indicator function. The connection with the local structure of sets in finite as well as in infinite dimensional spaces is also investigated. Special emphasis is given to a class of sets satisfying an external sphere condition, with locally uniform radius.

Keywords: Nonsmooth analysis, Bouligand normal cones, Clarke normal cones.

MSC: 49J52; 46C05

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