On the strong convergence of an inertial proximal algorithm with a time scale, Hessian-driven damping, and a Tikhonov regularization term

This paper concerns with convergence properties of an inertial proximal algorithm that contains a Tikhonov term regularization, time scale parameter, and a Hessian-driven damping in a Hilbert space.More precisely, we prove the strong convergence of the proximal algorithm obtained by temporal discretization of a continuous dynamic that we treated earlier in a previous work.We also obtain the convergence of the values to the global minimum of the objective function, and a strong convergence of the gradient and the velocity towards zero.Finally, we present a numerical example to illustrate our results.