Geodesic
Calmness of Nonsmooth Constraint Systems: Dual Conditions via Scalarized Exhausters
Journal of convex analysis, Tome 21 (2014) no. 2, pp. 507-534

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 49J52, 49J53, 90C30, 90C48
Mots-clés : Calmness, strict outer and strong slope, generalized differentiation, Hadamard directional derivatives, prox-regular set, scalarized exhausters 
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     author = {A. Uderzo},
     title = {Calmness of {Nonsmooth} {Constraint} {Systems:} {Dual} {Conditions} via {Scalarized} {Exhausters}},
     journal = {Journal of convex analysis},
     pages = {507--534},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2014},
     url = {http://geodesic.mathdoc.fr/item/JCA_2014_21_2_JCA_2014_21_2_a10/}
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A. Uderzo. Calmness of Nonsmooth Constraint Systems: Dual Conditions via Scalarized Exhausters. Journal of convex analysis, Tome 21 (2014) no. 2, pp. 507-534. http://geodesic.mathdoc.fr/item/JCA_2014_21_2_JCA_2014_21_2_a10/