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 $\mathcal{O}\left(1/n^2\right)$ 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.

中文翻译：

---

凸优化问题重球动力系统离散化优化算法收敛速度

在本文中，我们在无约束优化问题的设置中提出了新的数值算法，并证明了阶数的离散收敛速度$\mathcal{欧}\left(\mathrm{1个}/n^{\mathrm{2个}}\right)$在凸目标函数的迭代中。我们的优化算法是通过具有 Hessian 驱动阻尼的动力系统的离散化获得的。最后，为了验证理论结果，给出了一些数值实验。