The rate of convergence of optimization algorithms obtained via discretizations of heavy ball dynamical systems for convex optimization problems. (9th December 2022) - Alecsa, Cristian Daniel
Abstract : In this paper, we propose new numerical algorithms in the setting of unconstrained optimization problems and we prove the discrete rate of convergence of order O 1 / n 2 in the iterates of the convex objective function. Our optimization algorithms are obtained via discretizations from dynamical systems with Hessian-driven damping. Finally, some numerical experiments are presented in order to validate the theoretical results.