Convergence Rates of Inertial Primal-Dual Dynamical Methods for Separable Convex Optimization Problems

Abstract

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 $t\to +\infty$. The convergence rates are derived for different choices of the damping coefficients. We also show that the obtained results are robust under external perturbations.

References in corpus (3)

• A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights
• From differential equation solvers to accelerated first-order methods for convex optimization
• Exponential Stability of Primal-Dual Gradient Dynamics with Non-Strong Convexity

Cited by in corpus (1)

• Perturbed primal-dual dynamics with damping and time scaling coefficients for affine constrained convex optimization problems