Local convergence of inexact Gauss-Newton like methods for injective-overdetermined systems of equations under a majorant condition

TL;DR

This paper analyzes the local convergence of inexact Gauss-Newton like methods for solving injective-overdetermined systems, extending existing results using a majorant condition that relaxes convexity assumptions.

Contribution

It introduces a majorant condition with a non-convex derivative to extend and improve local convergence results for Gauss-Newton methods.

Findings

Convergence guaranteed under the new majorant condition.

Applicable to two important new cases.

Extends previous convergence analyses.

Abstract

In this paper, inexact Gauss-Newton like methods for solving injective-overdetermined systems of equations are studied. We use a majorant condition, defined by a function whose derivative is not necessarily convex, to extend and improve several existing results on the local convergence of the Gauss-Newton methods.In particular, this analysis guarantees the convergence of the methods for two important new cases.