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<p>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.</p>

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Strong and Fast Convergences for Damping, Scaling and Tikhonov Regularization

  • 期刊论文

  • 发表日期：

    2025年9月29日

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  • Hassan Riahi

摘要

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.