We investigate the asymptotic properties of the trajectories generated by a second-order dynamical system with Hessian driven damping and a Tikhonov regularization term in connection with the minimization of a smooth convex function in Hilbert spaces. We obtain fast convergence results for the function values along the trajectories. The Tikhonov regularization term enables the derivation of strong convergence results of the trajectory to the minimizer of the objective function of minimum norm.

中文翻译：

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具有 Hessian 驱动阻尼的二阶动力系统的 Tikhonov 正则化

我们研究了由具有 Hessian 驱动阻尼和 Tikhonov 正则化项的二阶动力系统生成的轨迹的渐近特性，这与希尔伯特空间中光滑凸函数的最小化有关。我们获得了沿轨迹的函数值的快速收敛结果。Tikhonov 正则化项能够将轨迹的强收敛结果推导到最小范数的目标函数的最小值。