Abstract: Our topic is the relationship between dynamical systems and optimization. This is a venerable, vast area in mathematics, counting among its many historical threads the study of gradient flow and the variational perspective on mechanics. We aim to build some new connections in this general area, studying aspects of gradient-based optimization from a continuous-time, variational point of view. We go beyond classical gradient flow to focus on second-order dynamics, aiming to show the relevance of such dynamics to optimization algorithms that not only converge, but converge quickly.
https://eta.impa.br/dl/PL012.pdf
本文讨论动力系统与最优化的关系。首先介绍加速梯度下降的Hamilton和Lagrange形式和加速的辛几何观点。然后介绍非凸优化，作者着重于上述动力系统的方法与基于梯度优化的鞍点逃逸率的联系。最后介绍随机动力系统，作者以欠阻尼Langevin扩散为例，作为加速梯度下降的一个类比。基于梯度的最优化及其在大规模统计推断问题中的应用目前非常活跃。
相关附件
20-PL012 Jordan
