Regularized Dynamical Systems for Finding Zeros of Generalized Monotone Operators

We propose regularized dynamical systems for finding zeros of generalized monotone operators in both continuous- and discrete-time settings. We establish strong convergence of the trajectories generated by such systems. Our results not only refine and extend the existing results, but also highlight examples where our results are applicable where current theory does not. Examples indicate that our methods exhibit varying convergence behaviors, with speeds that can be either faster or slower than the existing methods, depending on particular problems.