Local convergence analysis of a proximal Gauss-Newton method under a majorant condition

TL;DR

This paper analyzes the local convergence of a proximal Gauss-Newton method for penalized nonlinear least squares problems, establishing conditions under which convergence occurs and exploring special cases.

Contribution

It introduces a convergence analysis under a majorant condition, linking the problem's function to a majorant function, and examines two important special cases.

Findings

Convergence is guaranteed under a majorant condition.

Clear relationship established between the majorant and problem functions.

Convergence results derived for two special cases.

Abstract

In this paper, the proximal Gauss-Newton method for solving penalized nonlinear least squares problems is studied. A local convergence analysis is obtained under the assumption that the derivative of the function associated with the penalized least square problem satisfies a majorant condition. Our analysis provides a clear relationship between the majorant function and the function associated with the penalized least squares problem. The convergence for two important special cases is also derived.