Proximal determination of convex functions

2020/07/07 by Vilches, Emilio
#46N10 (Primary) 46N10 (Secondary) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2007.03798

Abstract

We provide comparison principles for convex functions through its proximal mappings. Consequently, we prove that the norm of the proximal operator determines a convex the function up to a constant. A new characterization of Lipschitzianity in terms of the proximal operator is given.

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