ON THE SIMULTANEOUS CONVERGENCE OF VALUES AND TRAJECTORIES OF CONTINUOUS INERTIAL DYNAMICS WITH TIKHONOV REGULARIZATION TO SOLVE CONVEX MINIMIZATION WITH AFFINE CONSTRAINTS - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2024

ON THE SIMULTANEOUS CONVERGENCE OF VALUES AND TRAJECTORIES OF CONTINUOUS INERTIAL DYNAMICS WITH TIKHONOV REGULARIZATION TO SOLVE CONVEX MINIMIZATION WITH AFFINE CONSTRAINTS

Zaki Chbani
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  • PersonId : 1015233
Hassan Riahi
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  • PersonId : 1365219

Résumé

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 linear constraints. The system is associated with the augmented Lagrangian formulation of the minimization problem. The corresponding dynamics brings into play three general time-varying parameters, which are respectively associated with viscous damping, extrapolation and temporal scaling. By appropriately adjusting these parameters, each with specific properties, 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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Dates et versions

hal-04511296 , version 1 (19-03-2024)

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  • HAL Id : hal-04511296 , version 1

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Zaki Chbani, Hassan Riahi, Fouad Battahi. ON THE SIMULTANEOUS CONVERGENCE OF VALUES AND TRAJECTORIES OF CONTINUOUS INERTIAL DYNAMICS WITH TIKHONOV REGULARIZATION TO SOLVE CONVEX MINIMIZATION WITH AFFINE CONSTRAINTS. 2024. ⟨hal-04511296⟩
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