PARAMETERIZED DOUGLAS-RACHFORD DYNAMICAL SYSTEM FOR MONOTONE INCLUSION PROBLEMS

Douglas-Rachford splitting method with resolvent operator is a renowned algorithm to solve monotone inclusion problem involving sum of two monotone operators. In this paper, we investigate a Douglas-Rachford-based dynamical systems designed to approach the solution sets of inclusion problems involving the sum of two maximally monotone operators. Our main aim is to use parametrized resolvent instead of classical resolvent as the Douglas-Rachford operator in the framework of preconditioning. The convergence of the orbit is demonstrated. We also add a Tikhonov regularized term (both inner and outer regularization) to obtain strong convergence of the induced orbit. ©2023 Applied Set-Valued Analysis and Optimization.