The long time behavior and the rate of convergence of symplectic convex algorithms obtained via splitting discretizations of inertial damping systems
arXiv:2001.10831
Abstract
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.
arXiv comment41 pages, 6 figures, 4 tables
References in corpus (6)
- A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights
- Splitting and composition methods in the numerical integration of differential equations
- A Dynamical Systems Perspective on Nesterov Acceleration
- Operator splitting for non-autonomous evolution equations
- First order optimization methods based on Hessian-driven Nesterov accelerated gradient flow
- Nesterov's method with decreasing learning rate leads to accelerated stochastic gradient descent