Local convergence analysis of inexact Gauss-Newton like methods under majorant condition

TL;DR

This paper analyzes the local convergence of inexact Gauss-Newton like methods for nonlinear least squares problems under a majorant condition, establishing convergence criteria and estimates.

Contribution

It provides a new convergence analysis framework linking the majorant function to the least squares problem, including convergence ball estimates.

Findings

Method is well-defined and converges under the majorant condition

Established relationship between majorant function and problem function

Derived convergence ball estimates for specific cases

Abstract

In this paper, we present a local convergence analysis of inexact Gauss-Newton like methods for solving nonlinear least squares problems. Under the hypothesis that the derivative of the function associated with the least square problem satisfies a majorant condition, we obtain that the method is well-defined and converges. Our analysis provides a clear relationship between the majorant function and the function associated with the least square problem. It also allows us to obtain an estimate of convergence ball for inexact Gauss-Newton like methods and some important, special cases.