From differential equation solvers to accelerated first-order methods for convex optimization

Convergence analysis of accelerated first-order methods for convex optimization problems are developed from the point of view of ordinary differential equation solvers. A new dynamical system, called Nesterov accelerated gradient (NAG) flow, is derived from the connection between acceleration mechan...

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Bibliographic Details
Published in:	Mathematical programming Vol. 195; no. 1-2; pp. 735 - 781
Main Authors:	Luo, Hao, Chen, Long
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2022 Springer Springer Nature B.V
Subjects:	Algorithms Calculus of Variations and Optimal Control; Optimization Combinatorics Computational geometry Convergence Convexity Differential equations Flow stability Full Length Paper Liapunov functions Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Mathematics of Computing Methods Numerical Analysis Optimization Solvers Theoretical Accelerated first-order methods 65B99 Convex optimization 90C25 65L20 Ordinary differential equation Exponential decay 37N40 Convergence analysis Lyapunov function
ISSN:	0025-5610, 1436-4646
Online Access:	Get full text
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