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.

Author information

Contact details are reproduced from the original publication and may be historical.

Emilio Vilches

Instituto de Ciencias de la Ingeniería, Universidad de O'Higgins, Rancagua, Chile

emilio.vilches@uoh.cl

Keywords

  • Proximal operator
  • determination of convex functions
  • Moreau decomposition
  • Legendre-Fenchel conjugate

Mathematics Subject Classification

49J52, 46N10

Suggested citation

E. Vilches. “Proximal Determination of Convex Functions.” Journal of Convex Analysis 28 (2021), No. 4, 1187–1192. https://doi.org/10.68381/jca28069

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Published by Heldermann Verlag, 2021. Rights now held by Banach Press.