https://mp.weixin.qq.com/s/Yi9KkCMFiKWOKbL9ystuWA 清华大学丘成桐数学科学中心 2022-01-19 19:56
From ODE Solvers to Accelerated Optimization Methods
Prof.Chen Long
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Organizer / 组织者
包承龙、史作强
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Speaker / 主讲人
Prof. Chen Long (Department of Mathematics, University of California, Irvine)
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Time / 时间
2022/01/21 08:30-10:00 am.
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Venue / 地点
Tencent Meeting
ID：904-824-431 Passcode：220121
Abstract
Convergence analysis of accelerated first-order methods for convex optimization problems are presented from the point of view of ordinary differential equation (ODE) solvers. We first take another look at the acceleration phenomenon via A-stability theory for ODE solvers and present an explanation by transformation of spectrum to the complex plane. After that, we present the Lyapunov framework for dynamical system and introduce the strong Lyapunov condition. Many existing continuous convex optimization models, such as gradient flow, heavy ball system, Nesterov accelerated gradient flow, and dynamical inertial Newton system etc, are addressed and analyzed in this framework.
This is a joint work with Dr. Hao Luo at Peking University.
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