Abstract

We show that prox-regular functions are locally uniquely determined by their subgradients i.e. if two functions are prox-regular at xˉ\bar{x} for vˉ\bar{v}, then in a neighborhood of (xˉ,vˉ)(\bar{x}, \bar{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).

Author information

Contact details are reproduced from the original publication and may be historical.

Sanath Boralugoda

Dept. of Mathematics, University of Alberta, Edmonton, Alb. T6G 2G1, Canada

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

Mathematics Subject Classification

49A52, 58C06, 58C20; 90C30

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Suggested citation

S. Boralugoda, R. A. Poliquin. “Local Integration of Prox-Regular Functions in Hilbert Spaces.” Journal of Convex Analysis 13 (2006), No. 1, 27–36. https://doi.org/10.68381/jca13002

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Published by Heldermann Verlag, 2006. Rights now held by Banach Press LLC.