Geodesic
Prox-Regularity and Stability of the Proximal Mapping
Journal of convex analysis, Tome 14 (2007) no. 3, pp. 589-606

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

Fundamental insights into the properties of a function come from the study of its Moreau envelopes and Proximal point mappings. In this paper we examine the stability of these two objects under several types of perturbations. In the simplest case, we consider tilt-perturbations, i.e. perturbations which correspond to adding a linear term to the objective function. We show that for functions that have single-valued Lipschitz continuous proximal mappings, in particular for prox-regular functions, tilt-perturbations result in stable, i.e. single-valued Lipschitz continuous, proximal point mappings.
Classification : 49A52, 58C06, 58C20, 90C30
Mots-clés : Prox-regular, proximal mapping, Moreau envelope, stability, convex, convexly composite, strongly amenable, compatible parameterization, perturbations, sensitivity analysis 
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     author = {W. L. Hare and R. A. Poliquin},
     title = {Prox-Regularity and {Stability} of the {Proximal} {Mapping}},
     journal = {Journal of convex analysis},
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     publisher = {mathdoc},
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     number = {3},
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     url = {http://geodesic.mathdoc.fr/item/JCA_2007_14_3_JCA_2007_14_3_a6/}
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W. L. Hare; R. A. Poliquin. Prox-Regularity and Stability of the Proximal Mapping. Journal of convex analysis, Tome 14 (2007) no. 3, pp. 589-606. http://geodesic.mathdoc.fr/item/JCA_2007_14_3_JCA_2007_14_3_a6/