Accelerated Gradient Methods Combining Tikhonov Regularization with Geometric Damping Driven by the Hessian

In a Hilbert framework, for general convex differentiable optimization, we consider accelerated gradient dynamics combining Tikhonov regularization with Hessian-driven damping. The temporal discretization of these leads to new class first-order optimization algorithms favorable properties. parameter is assumed tend zero as time tends infinity, which preserves equilibria. presence the term induces strong property convexity vanishes asymptotically. To take advantage fast convergence rates attached heavy ball method in strongly case, inertial where viscous damping coefficient proportional square root parameter, and hence converges zero. geometric damping, controlled by Hessian function be minimized, attenuation oscillations. Under an appropriate setting parameters, based on Lyapunov’s analysis, show that trajectories provide at same several remarkable properties: values, gradients towards zero, minimum norm minimizer. We corresponding proximal share properties continuous dynamics. numerical illustrations confirm results obtained. This study extends previous paper authors regarding similar problems without driven