Fast Convergence of Dynamical ADMM via Time Scaling of Damped Inertial Dynamics

Hedy Attouch (), Zaki Chbani (), Jalal Fadili () and Hassan Riahi ()
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Hedy Attouch: Université Montpellier
Zaki Chbani: Cadi Ayyad University
Jalal Fadili: ENSICAEN, UNICAEN, CNRS, GREYC
Hassan Riahi: Cadi Ayyad University

Journal of Optimization Theory and Applications, 2022, vol. 193, issue 1, No 30, 704-736

Abstract: Abstract In this paper, we propose in a Hilbertian setting a second-order time-continuous dynamic system with fast convergence guarantees to solve structured convex minimization problems with an affine constraint. The system is associated with the augmented Lagrangian formulation of the minimization problem. The corresponding dynamics brings into play three general time-varying parameters, each with specific properties, and which are, respectively, associated with viscous damping, extrapolation and temporal scaling. By appropriately adjusting these parameters, we develop a Lyapunov analysis which provides fast convergence properties of the values and of the feasibility gap. These results will naturally pave the way for developing corresponding accelerated ADMM algorithms, obtained by temporal discretization.

Keywords: Augmented Lagrangian; ADMM; Damped inertial dynamics; Convex constrained minimization; Convergence rates; Lyapunov analysis; Nesterov accelerated gradient method; Temporal scaling (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-021-01859-2

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