A dual based semismooth Newton method for a class of sparse Tikhonov regularization

TL;DR

This paper introduces a dual-based semismooth Newton method for sparse Tikhonov regularization that maintains dataset structure and achieves global convergence with superlinear rate, demonstrating effectiveness on high-dimensional data.

Contribution

The paper develops a novel DSSN method that preserves dataset structure and proves its global convergence with superlinear rate, addressing computational challenges in sparse Tikhonov regularization.

Findings

DSSN method is globally convergent with R-superlinear rate.

Effective on high-dimensional datasets for sparse regularization.

Maintains dataset structure without enlargement.

Abstract

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.