Fouad Battahi, Zaki Chbani, Hassan Riahi, On the simultaneous convergence of values and trajectories of continuous inertial dynamics with Tikhonov regularization to solve convex minimization with affine constraints
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DOI: 10.23952/asvao.7.2025.3.06
Volume 7, Issue 3, 1 December 2025, Pages 373-392
Abstract. In this paper, we propose in a Hilbertian setting a second-order time-continuous dynamic system with fast convergence guarantees to solve general convex minimization problems with linear constraints. The system is associated with the augmented Lagrangian formulation of a minimization problem. The corresponding dynamic involves 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 naturally pave the way for developing corresponding accelerated ADMM algorithms, obtained by temporal discretization.
How to Cite this Article:
F. Battahi, Z. Chbani, H. Riahi, On the simultaneous convergence of values and trajectories of continuous inertial dynamics with Tikhonov regularization to solve convex minimization with affine constraints, Appl. Set-Valued Anal. Optim. 7 (2025), 373-392.