具有海森矩阵驱动阻尼的二阶动力系统的蒂霍诺夫正则化
Tikhonov regularization of a second order dynamical system with Hessian driven damping.
作者信息
Boţ Radu Ioan, Csetnek Ernö Robert, László Szilárd Csaba
机构信息
Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria.
Department of Mathematics, Technical University of Cluj-Napoca, Memorandumului 28, Cluj-Napoca, Romania.
出版信息
Math Program. 2021;189(1-2):151-186. doi: 10.1007/s10107-020-01528-8. Epub 2020 Jun 11.
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.
我们研究了在希尔伯特空间中，与一个光滑凸函数的最小化相关的、具有黑塞驱动阻尼和蒂霍诺夫正则化项的二阶动力系统所生成轨迹的渐近性质。我们得到了沿轨迹的函数值的快速收敛结果。蒂霍诺夫正则化项使得能够推导出轨迹到最小范数目标函数极小值点的强收敛结果。
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