Journal of Convex Analysis 13 (2006), No. 1, 027--036
Copyright Heldermann Verlag 2006
Local Integration of Prox-Regular 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 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).
Keywords: Prox-regular, primal-lower-nice, pln, regularization, nonsmooth analysis, integration of subgradients, subgradient mappings, subgradient localization, amenable functions, proximal subgradients, Moreau envelopes, proximal mapping.
MSC: 49A52, 58C06, 58C20; 90C30
[ Fulltext-pdf (304 KB)] for subscribers only.