##### Department of Mathematics,

University of California San Diego

****************************

### Math 278C - Optimization and Data Science

## Long Chen

#### UC Irvine

## From ODE solvers to accelerated first-order methods for convex optimization

##### 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 a revealing spectrum analysis for quadratic programming. 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. Then we present convergence analyses of optimization algorithms obtained from implicit or explicit methods of underlying dynamical systems.

Host: Jiawang Nie

### January 12, 2022

### 3:00 PM

https://ucsd.zoom.us/j/94927846567

Meeting ID: 949 2784 6567

Password: 278CWN22

****************************