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

Abstract : In this paper, we propose in a Hilbertian setting a second-order timecontinuous 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.
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https://hal.archives-ouvertes.fr/hal-03177752
Contributor : Jalal Fadili <>
Submitted on : Tuesday, March 23, 2021 - 1:58:35 PM
Last modification on : Wednesday, April 28, 2021 - 6:03:39 PM

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  • HAL Id : hal-03177752, version 1

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Hedy Attouch, Zaki Chbani, Jalal M. Fadili, Hassan Riahi. Fast convergence of dynamical ADMM via time scaling of damped inertial dynamics. Journal of Optimization Theory and Applications, Springer Verlag, inPress. ⟨hal-03177752⟩

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