Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Giovanni Colombo

Dip. di Matematica Pura ed Applicata, Università di Padova, Via Belzoni 7, 35131 Padova, Italy

Vladimir V. Goncharov

SISSA, via Beirut 4, 34013 Trieste, Italy
and: Institute of System Dynamics and Control Theory, Russian Academy of Sciences, ul. Lermontov 134, 664033 Irkutsk, Russia

Keywords

  • Nonsmooth analysis
  • Bouligand normal cones
  • Clarke normal cones

Mathematics Subject Classification

49J52; 46C05

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Suggested citation

G. Colombo, V. V. Goncharov. “Variational Inequalities and Regularity Properties of Closed Sets in Hilbert Spaces.” Journal of Convex Analysis 8 (2001), No. 1, 197–221. https://doi.org/10.68381/jca08009

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Published by Heldermann Verlag, 2001. Rights now held by Banach Press.