The strong convergence of the trajectory of a Tikhonov regularized inertial primal-dual dynamical system with a slow damping

We propose a Tikhonov regularized inertial primal-dual dynamical system with a slow damping $\frac{\alpha}{t^q}$, where the inertial term is introduced only for the primal variable, for the linearly constrained convex optimization problem in Hilbert spaces. Under a suitable assumption on the underlying parameters, by a Lyapunov analysis approach, we prove the strong convergence of the trajectory of the proposed system to the minimal norm primal-dual solution of the problem, along with convergence rate results for the primal-dual gap, the objective residual and the feasibility violation. In Section 4, , we perform some numerical experiments to illustrate the theoretical results. Finaly, we give a conclusion in Section 5.