Moreau’s Decomposition Theorem Revisited

  • J.B. Hiriart-Urruty

    U.F.R. Mathématiques, Informatique, Gestion, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex, France
  • Ph. Plazanet

    Dépanement de Mathématiques Appliquées, E.N.S.J.C.A., 49 Avenue Léon Blum, 31056 Toulouse Cédex, France

Abstract

Given two convex functions and on a Hilbert space, verifying , we show there necessarily exists a lower‐semicontinuous convex function such that and . An explicit formulation of is given as a deconvolution of a convex function by another one. The approach taken here as well as the way of factorizing and shed a new light on what is known as Moreau’s theorem in the literature on Convex Analysis.

Cite this article

J.B. Hiriart-Urruty, Ph. Plazanet, Moreau’s Decomposition Theorem Revisited. Ann. Inst. H. Poincaré Anal. Non Linéaire 6 (1989), pp. 325–338

DOI 10.1016/S0294-1449(17)30028-8