OPERATOR SPLITTING SCHEMES THROUGH A REGULARIZATION APPROACH

We propose a new algorithm for finding a zero of the sum of two monotone operators. It works by only requiring the evaluation of the resolvents of each of the operators individually, rather than the resolvent of their sum. We leverage then the connection with a co-coerciveness related operator, obtained by the sum and composition of Yosida regularization and reflected resolvents of the involved operators, to derive both a weak and a strong convergence results. The latter are provided by means of Krasnoselskii and Halpern celebrated classical Theorems.