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

• 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

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...