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In this paper we propose new numerical algorithms in the setting ofunconstrained optimization problems and we study the rate of convergence in theiterates of the objective function. Furthermore, our algorithms are based uponsplitting and symplectic methods and they preserve the energy properties of theinherent continuous dynamical system that contains a Hessian perturbation. Atthe same time, we show that Nesterov gradient method is equivalent to aLie-Trotter splitting applied to a Hessian driven damping system. Finally, somenumerical experiments are presented in order to validate the theoreticalresults.

The long time behavior and the rate of convergence of symplectic convex algorithms obtained via splitting discretizations of inertial damping systems