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arXiv · 2109.13467

A unified differential equation solver approach for separable convex optimization: splitting, acceleration and nonergodic rate

Hao Luo·Zihang Zhang
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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.

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Hao Luo, Zihang Zhang. 2021-09-28. A unified differential equation solver approach for separable convex optimization: splitting, acceleration and nonergodic rate. https://arxiv.org/abs/2109.13467

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