PARTIAL REGULARIZATION OF THE SUM OF 2 MAXIMAL MONOTONE-OPERATORS

To find a zero of the sum of two maximal monotone operators, we analyz e a two-steps algorithm where the problem is first approximated by a r egularized one and the regularization parameter is then reduced to con verge to a solution of the original problem. We give a formal proof of the convergence which, in that case, is not ergodic. The main result is a generalization of one given by Brezis [4] who has considered oper ators of the form I + A + B. Additional insight on the underlying exis tence problems and on the kind of convergence we aim at are given with the hypothesis that one of the two operators is strongly monotone. A general scheme for the decomposition of large scale convex programs is then induced.