A dynamical alternating direction method of multipliers for two-block optimization problems

In this paper, we propose a dynamical alternating direction method of multipliers (ADMM) for two-block separable optimization problems. The well-known classical ADMM can be obtained after the time discretization of the dynamical system. Under suitable conditions, we prove that the trajectory asympto...

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Bibliographic Details
Published in:Nonlinear dynamics 2023-04, Vol.111 (7), p.6557-6583
Main Authors: Chao, Miantao, Liu, Liqun
Format: Article
Language:English
Subjects:
Algorithms
Automotive Engineering
Classical Mechanics
Control
Convergence
Dynamical Systems
Engineering
Lagrangian function
Mechanical Engineering
Multipliers
Optimization
Original Paper
Saddle points
Vibration
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Summary:In this paper, we propose a dynamical alternating direction method of multipliers (ADMM) for two-block separable optimization problems. The well-known classical ADMM can be obtained after the time discretization of the dynamical system. Under suitable conditions, we prove that the trajectory asymptotically converges to a saddle point of the Lagrangian function of the problems. When the coefficient matrices in the constraint are the identity matrices, we prove the worst-case O ( 1 t ) convergence rate in ergodic sense.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-022-08174-z