A Gradient-Like Regularized Dynamics for Monotone Equilibrium Problems.

In this paper, a gradient-like regularized dynamical system associated with a monotone equilibrium problem is studied. First, we give a rigorous proof of the existence and uniqueness of the strong global solution to the dynamical system. Then, we obtain strong convergence of the generated trajectories to a solution of the original equilibrium. A time discretization of the dynamical system provides a strongly convergent iterative regularization gradient-type method with relaxation parameters. Finally, the performance of the regularized dynamical system approach is illustrated by numerical experiments. [ABSTRACT FROM AUTHOR]