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.
Penot , Proximal mappings, Journal of Approximation Theory, 94 (1998), 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.