Geodesic
Local Integration of Prox-Regular Functions in Hilbert Spaces
Journal of convex analysis, Tome 13 (2006) no. 1, pp. 27-36
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We show that prox-regular functions are locally uniquely determined by their subgradients i.e. if two functions are prox-regular at x* for v*, then in a neighborhood of (x*, v*), the functions differ by an additive constant. The class of prox-regular functions includes all convex functions, all qualified convexly composite functions (i.e. with an appropriate constraint qualification) and all pln functions. This result represents an improvement over previous results since the class of prox-regular functions is strictly bigger than the class of pln functions (an example is provided in this paper).
Classification : 49A52, 58C06, 58C20, 90C30
Mots-clés : Prox-regular, primal-lower-nice, pln, regularization, nonsmooth analysis, integration of subgradients, subgradient mappings, subgradient localization, amenable functions, proximal subgradients, Moreau envelopes, proximal mapping 
@article{JCA_2006_13_1_JCA_2006_13_1_a1,
     author = {S. Boralugoda and R. A. Poliquin},
     title = {Local {Integration} of {Prox-Regular} {Functions} in {Hilbert} {Spaces}},
     journal = {Journal of convex analysis},
     pages = {27--36},
     year = {2006},
     volume = {13},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2006_13_1_JCA_2006_13_1_a1/}
}
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S. Boralugoda; R. A. Poliquin. Local Integration of Prox-Regular Functions in Hilbert Spaces. Journal of convex analysis, Tome 13 (2006) no. 1, pp. 27-36. http://geodesic.mathdoc.fr/item/JCA_2006_13_1_JCA_2006_13_1_a1/