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