Strong and Fast Convergences for Damping, Scaling and Tikhonov Regularization

Hassan Riahi ()
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Hassan Riahi: Cadi Ayyad University, Faculty of Sciences Semlalia

Journal of Optimization Theory and Applications, 2026, vol. 208, issue 1, No 19, 29 pages

Abstract: Abstract To reach a minimizer of a convex and continuously differentiable function, we investigate the long-time behavior of the trajectories of a vanishing damped nonlinear dynamical system with a positive viscous damping coefficient on the velocity term, a scaling coefficient on the gradient of this function and an appropriate Tikhonov regularization parameter. We justify that each of these parameters plays its relative role in improving the asymptotic behavior of the solution of the proposed dynamical system. In doing so, we improve some recent results on the subject. In addition, this paper generates new results ensuring better convergence of values, gradients and velocities.

Keywords: Convex optimization; Dynamical system; Viscous damping; Time scaling; Tikhonov regularization; Fast convergence; Strong convergence; 37N40; 46N10; 49M30; 65K05; 65K10; 90B50; 90C25 (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/s10957-025-02842-x

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