Journal of Convex Analysis 28 (2021), No. 4, 1187--1192
Copyright Heldermann Verlag 2021
Proximal Determination of Convex Functions
Emilio Vilches
Instituto de Ciencias de la Ingenierķa, Universidad de O'Higgins, Rancagua, Chile
emilio.vilches@uoh.cl
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.
Keywords: Proximal operator, determination of convex functions, Moreau decomposition, Legendre-Fenchel conjugate.
MSC: 49J52, 46N10.
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