Abstract

Variationally convex functions and prox-regular functions are placed in a single framework that coordinates and enhances the many connections between them. Their characterization in terms of monotonicity properties of subgradient mappings is confirmed by a more informative argument than has previously been offered, which yields more a definitive result.

Author information

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

R. Tyrrell Rockafellar

Department of Mathematics, University of Washington, Seattle, U.S.A.

rtr@uw.edu

Keywords

  • Variational convexity
  • prox-regularity
  • local subdifferential monotonicity
  • uniform quadratic growth
  • second-order variational analysis

Mathematics Subject Classification

49J53, 46N10

Suggested citation

R. T. Rockafellar. “Variational Convexity and Prox-Regularity.” Journal of Convex Analysis 33 (2026), No. 3&4, 1049–1060. https://doi.org/10.68381/jca33055

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Published by Heldermann Verlag, 2026. Rights now held by Banach Press.