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DOI: 10.23952/cot.2025.2
Received January 26, 2024; Accepted March 27, 2024; Published online October 22, 2024
Abstract. We propose new algorithms for finding a zero of the sum of two monotone operators. They work 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 weak and strong convergence results. The latter are provided by means of Krasnoselskii and Halpern celebrated classical Theorems. Two other weak convergence results using new algorithms based on the modifications of a forward-backward splitting method introduced.
How to Cite this Article:
A. Moudafi, Operator splitting schemes through a regularization approach, Commun. Optim. Theory 2025 (2025) 2.