Computing the resolvent of composite operators

Abdellatif Moudafi

doi:10.4067/S0719-06462014000300007

Authors

Abdellatif Moudafi L.S.I.S, Aix Marseille Université, U.F.R Sciences, Domaine Universitaire de Saint-Jérôme. Avenue Escadrille Normandie-Niemen, 13397 MARSEILLE CEDEX 20,

DOI:

https://doi.org/10.4067/S0719-06462014000300007

Keywords:

maximal monotone operators, KM-algorithm, Yosida regularization, Douglas-Rachford algorithm, Dykstra-like method

Abstract

Based in a very recent paper by Micchelli et al. [8], we present an algorithmic approach for computing the resolvent of composite operators: the composition of a monotone operator and a continuous linear mapping. The proposed algorithm can be used, for example, for solving problems arising in image processing and traffic equilibrium. Fur- thermore, our algorithm gives an alternative to Dykstra-like method for evaluating the resolvent of the sum of two maximal monotone operators.