Skip to yearly menu bar Skip to main content


Convergence analysis of ODE models for accelerated first-order methods via positive semidefinite kernels

Jungbin Kim · Insoon Yang

Great Hall & Hall B1+B2 (level 1) #1116
[ ]
[ Paper [ Slides [ Poster [ OpenReview
Wed 13 Dec 3 p.m. PST — 5 p.m. PST


We propose a novel methodology that systematically analyzes ordinary differential equation (ODE) models for first-order optimization methods by converting the task of proving convergence rates into verifying the positive semidefiniteness of specific Hilbert-Schmidt integral operators. Our approach is based on the performance estimation problems (PEP) introduced by Drori and Teboulle. Unlike previous works on PEP, which rely on finite-dimensional linear algebra, we use tools from functional analysis. Using the proposed method, we establish convergence rates of various accelerated gradient flow models, some of which are new. As an immediate consequence of our framework, we show a correspondence between minimizing function values and minimizing gradient norms.

Chat is not available.