Strong asymptotic convergence of a slowly damped inertial primal-dual dynamical system controlled by a Tikhonov regularization term

Abstract

We propose a slowly damped inertial primal-dual dynamical system controlled by a Tikhonov regularization term, where the inertial term is introduced only for the primal variable, for the linearly constrained convex optimization problem in a Hilbert space. Under mild conditions on the underlying parameters, by a Lyapunov analysis approach, we prove the strong asymptotic convergence of the trajectory of the proposed dynamic to the minimal norm element of the primal-dual solution set of the problem, along with convergence rate results for the primal-dual gap, the objective residual and the feasibility violation. We perform some numerical experiments to illustrate the theoretical findings.