Journal of Convex Analysis 33 (2026), No. 3&4, 1049--1060
Copyright Heldermann Verlag 2026
Variational Convexity and Prox-Regularity
R. Tyrrell Rockafellar
Department of Mathematics, University of Washington, Seattle, U.S.A.
rtr@uw.edu
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.
Keywords: Variational convexity, prox-regularity, local subdifferential monotonicity, uniform quadratic growth, second-order variational analysis.
MSC: 49J53, 46N10.
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