Level proximal subdifferential characterizes variational convexity via local firm nonexpansiveness of proximal mappings and supports local convergence of proximal gradient methods to minimizers for variationally convex functions.
Moreau , Proximit´ e et dualit´ e dans un espace hilbertien , Bulletin de la Soci´ et´ e Math´ ematique de France, 93 (1965), pp
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Level proximal subdifferential, variational convexity, and pointwise quadratic approximation
Level proximal subdifferential characterizes variational convexity via local firm nonexpansiveness of proximal mappings and supports local convergence of proximal gradient methods to minimizers for variationally convex functions.