论文标题
一种基于双重的半齿牛顿方法，用于一类稀疏的Tikhonov正则化
A dual based semismooth Newton method for a class of sparse Tikhonov regularization
论文作者
论文摘要
众所周知，Tikhonov正则化是解决不良问题的最常用方法之一。最广泛应用的方法之一是基于构建一个新数据集，其样本大小大于原始数据集。放大的样本量可能带来其他计算困难。在本文中，我们旨在充分利用Tikhonov正则化，并开发出双重的半齿牛顿（DSSN）方法，而不会破坏数据集的结构。从理论的角度来看，我们将证明\ blue {dssn方法是一种全球收敛的方法，至少是r-per-perlinear的收敛速率。}在数值计算方面，我们通过求解一类稀疏的Tikhonov和高清数据量的稀疏Tikhonov通过求解DSSN方法的性能。
It is well known that Tikhonov regularization is one of the most commonly used methods for solving ill-posed problems. One of the most widely applied approaches is based on constructing a new dataset whose sample size is greater than the original one. The enlarged sample size may bring additional computational difficulties. In this paper, we aim to make full use of Tikhonov regularization and develop a dual based semismooth Newton (DSSN) method without destroying the structure of dataset. From the point of view of theory, we will show that \blue{the DSSN method is a globally convergent method with at least R-superlinear rate of convergence.} In the numerical computation aspect, we evaluate the performance of the DSSN method by solving a class of sparse Tikhonov regularization with high-dimensional datasets.
