Fast convergence of dynamical ADMM via time scaling of damped inertial\n dynamics

2021/03/23 by Hédy Attouch, Zaki Chbani, Attouch, Hedy +5 · 4 citations
Computer Science · Engineering · #Adaptive Control of Nonlinear Systems #Distributed Control Multi-Agent Systems #FOS: Mathematics #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.2103.12675

openalex publication_date 2021/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we propose in a Hilbertian setting a second-order\ntime-continuous dynamic system with fast convergence guarantees to solve\nstructured convex minimization problems with an affine constraint. The system\nis associated with the augmented Lagrangian formulation of the minimization\nproblem. The corresponding dynamics brings into play three general time-varying\nparameters, each with specific properties, and which are respectively\nassociated with viscous damping, extrapolation and temporal scaling. By\nappropriately adjusting these parameters, we develop a Lyapunov analysis which\nprovides fast convergence properties of the values and of the feasibility gap.\nThese results will naturally pave the way for developing corresponding\naccelerated ADMM algorithms, obtained by temporal discretization.\n

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• Inertial Primal Dual Dynamics with Hessian-driven Damping for Saddle Point Problems
• Fast convergence of dynamical systems with implicit Hessian damping and Tikhonov regularization
• Preconditioned primal-dual dynamics in convex optimization: non-ergodic convergence rates

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