Abstract

This paper considers the problem of establishing sufficient conditions for calmness, a property describing the Lipschitzian behaviour of set-valued mappings, whose introduction was strongly motivated by needs in optimization and mathematical programming. The study of such problem is undertaken in the specific context of nonsmooth constraint systems. As analysis tools, proper adaptations of known dual constructions in generalized differentiation theory and abstract convex analysis are employed. By means of them, some settings are singled out, where it is possible to formulate calmness conditions, in the case the set appearing in the constraint system is convex or prox-regular.

Author information

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

Amos Uderzo

Dip. di Matematica e Applicazioni, Università di Milano-Bicocca, Via Cozzi 53, 20125 Milano, Italy

amos.uderzo@unimib.it

Keywords

  • Calmness
  • strict outer and strong slope
  • generalized differentiation
  • Hadamard directional derivatives
  • prox-regular set
  • scalarized exhausters

Mathematics Subject Classification

49J52; 49J53, 90C30, 90C48

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Suggested citation

A. Uderzo. “Calmness of Nonsmooth Constraint Systems: Dual Conditions via Scalarized Exhausters.” Journal of Convex Analysis 21 (2014), No. 2, 507–534. https://doi.org/10.68381/jca21027

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Published by Heldermann Verlag, 2014. Rights now held by Banach Press.