论文标题
关于Tikhonov正规化二阶动力学系统的轨迹的强烈收敛，渐近消失了阻尼
On the strong convergence of the trajectories of a Tikhonov regularized second order dynamical system with asymptotically vanishing damping
论文作者
论文摘要
本文处理了一个二阶动力学系统，其中包含Tikhonov正则化项的消失阻尼，与凸面可区分函数$ g $的最小化问题有关。 我们表明，对于适当的Tikhonov正则化参数，生成的轨迹中目标函数的值快速收敛到目标函数的全局最小值，而动态系统生成的轨迹却微弱地收敛到目标函数的最小化器。我们还获得了速度向零和一些积分估计的快速收敛。然而，我们的主要目标是在\ cite {abcr}和\ cite {al-nemkoz}中扩展和改善一些最新结果，即从目标函数$ g $的$ \ argmin $集中从$ \ argmin $ sep中汇给最小规范的强烈收敛。我们的分析还表明，阻尼系数和Tikhonov正则化系数密切相关。
This paper deals with a second order dynamical system with vanishing damping that contains a Tikhonov regularization term, in connection to the minimization problem of a convex Fréchet differentiable function $g$. We show that for appropriate Tikhonov regularization parameters the value of the objective function in a generated trajectory converges fast to the global minimum of the objective function and a trajectory generated by the dynamical system converges weakly to a minimizer of the objective function. We also obtain the fast convergence of the velocities towards zero and some integral estimates. Nevertheless, our main goal is to extend and improve some recent results obtained in \cite{ABCR} and \cite{AL-nemkoz} concerning the strong convergence of the generated trajectories to an element of minimal norm from the $\argmin$ set of the objective function $g$. Our analysis also reveals that the damping coefficient and the Tikhonov regularization coefficient are strongly correlated.
