A unified differential equation solver approach for separable convex optimization: splitting, acceleration and nonergodic rate
Abstract
This paper provides a self-contained ordinary differential equation solver approach for separable convex optimization problems. A novel primal-dual dynamical system with built-in time rescaling factors is introduced, and the exponential decay of a tailored Lyapunov function is established. Then several time discretizations of the continuous model are considered and analyzed via a unified discrete Lyapunov function. Moreover, two families of accelerated proximal alternating direction methods of multipliers are obtained, and nonergodic optimal mixed-type convergence rates shall be proved for the primal objective residual, the feasibility violation and the Lagrangian gap. Finally, numerical experiments are provided to validate the practical performances.
Cite
@article{arxiv.2109.13467,
title = {A unified differential equation solver approach for separable convex optimization: splitting, acceleration and nonergodic rate},
author = {Hao Luo and Zihang Zhang},
journal= {arXiv preprint arXiv:2109.13467},
year = {2023}
}