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

Autor:	Alecsa, Cristian Daniel
Rok vydání:	2020
Předmět:	Mathematics - Optimization and Control
Druh dokumentu:	Working Paper
Popis:	In this paper we propose new numerical algorithms in the setting of unconstrained optimization problems and we study the rate of convergence in the iterates of the objective function. Furthermore, our algorithms are based upon splitting and symplectic methods and they preserve the energy properties of the inherent continuous dynamical system that contains a Hessian perturbation. At the same time, we show that Nesterov gradient method is equivalent to a Lie-Trotter splitting applied to a Hessian driven damping system. Finally, some numerical experiments are presented in order to validate the theoretical results. Comment: 41 pages, 6 figures, 4 tables
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2001.10831 Zobrazit plný text záznamu View this record from Arxiv