
Journal of Convex Analysis 13 (2006), No. 1, 027036 Copyright Heldermann Verlag 2006 Local Integration of ProxRegular Functions in Hilbert Spaces Sanath Boralugoda Dept. of Mathematics, University of Alberta, Edmonton, Alb. T6G 2G1, Canada René A. Poliquin Dept. of Mathematics, University of Alberta, Edmonton, Alb. T6G 2G1, Canada rene.poliquin@ualberta.ca We show that proxregular functions are locally uniquely determined by their subgradients i.e. if two functions are proxregular at x* for v*, then in a neighborhood of (x*, v*), the functions differ by an additive constant. The class of proxregular 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 proxregular functions is strictly bigger than the class of pln functions (an example is provided in this paper). Keywords: Proxregular, primallowernice, pln, regularization, nonsmooth analysis, integration of subgradients, subgradient mappings, subgradient localization, amenable functions, proximal subgradients, Moreau envelopes, proximal mapping. MSC: 49A52, 58C06, 58C20; 90C30 [ Fulltextpdf (304 KB)] for subscribers only. 