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Journal of Convex Analysis 21 (2014), No. 2, 507--534
Copyright Heldermann Verlag 2014



Calmness of Nonsmooth Constraint Systems: Dual Conditions via Scalarized Exhausters

Amos Uderzo
Dip. di Matematica e Applicazioni, UniversitÓ di Milano-Bicocca, Via Cozzi 53, 20125 Milano, Italy
amos.uderzo@unimib.it



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.

Keywords: Calmness, strict outer and strong slope, generalized differentiation, Hadamard directional derivatives, prox-regular set, scalarized exhausters.

MSC: 49J52; 49J53, 90C30, 90C48

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