论文标题
通过惯性阻尼系统的离散化获得的符号凸算法的长时间行为和融合率
The long time behavior and the rate of convergence of symplectic convex algorithms obtained via splitting discretizations of inertial damping systems
论文作者
论文摘要
在本文中，我们在不受限制的优化问题的情况下提出了新的数值算法，并研究了目标函数迭代中的收敛速度。此外，我们的算法基于分裂和符号方法，它们保留了包含Hessian扰动的固有连续动力系统的能量。同时，我们表明Nesterov梯度方法等于应用于Hessian驱动的阻尼系统的Lie-Trotter分裂。最后，提供了一些数值实验，以验证理论结果。
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.
