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, FrancePh. 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