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

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.