In this paper, we propose a second-order continuous primal-dual dynamical system with time-dependent positive damping terms for a separable convex optimization problem with linear equality constraints. By the Lyapunov function approach, we investigate asymptotic properties of the proposed dynamical system as the time t→+∞. The convergence rates are derived for different choices of the damping coefficients. We also show that the obtained results are robust under external perturbations.
@article{arxiv.2007.12428,
title = {Convergence Rates of Inertial Primal-Dual Dynamical Methods for Separable Convex Optimization Problems},
author = {Xin He and Rong Hu and Ya-Ping Fang},
journal= {arXiv preprint arXiv:2007.12428},
year = {2020}
}