A Tuning-Free Primal-Dual Splitting Algorithm for Large-Scale Semidefinite Programming
Optimization and Control
2024-02-02 v1
Abstract
This paper proposes and analyzes a tuning-free variant of Primal-Dual Hybrid Gradient (PDHG), and investigates its effectiveness for solving large-scale semidefinite programming (SDP). The core idea is based on the combination of two seemingly unrelated results: (1) the equivalence of PDHG and Douglas-Rachford splitting (DRS); (2) the asymptotic convergence of non-stationary DRS. This combination provides a unified approach to analyze the convergence of generic adaptive PDHG, including the proposed tuning-free algorithm and various existing ones. Numerical experiments are conducted to show the performance of our algorithm, highlighting its superior convergence speed and robustness in the context of SDP.
Cite
@article{arxiv.2402.00311,
title = {A Tuning-Free Primal-Dual Splitting Algorithm for Large-Scale Semidefinite Programming},
author = {Yinjun Wang and Haixiang Lan and Yinyu Ye},
journal= {arXiv preprint arXiv:2402.00311},
year = {2024}
}