Local convergence of the Gauss-Newton method for injective-overdetermined systems of equations under a majorant condition

TL;DR

This paper provides a local convergence analysis of the Gauss-Newton method for injective-overdetermined systems under a majorant condition, establishing convergence properties without convexity assumptions.

Contribution

It introduces a novel convergence analysis framework for the Gauss-Newton method under a majorant condition without requiring convexity of the derivative.

Findings

Convergence and rate results are established.

Optimal convergence radius is determined.

Conditions for solution uniqueness are identified.

Abstract

A local convergence analysis of the Gauss-Newton method for solving injective-overdetermined systems of nonlinear equations under a majorant condition is provided. The convergence as well as results on its rate are established without a convexity hypothesis on the derivative of the majorant function. The optimal convergence radius, the biggest range for uniqueness of the solution along with some other special cases are also obtained.range for uniqueness of the solution along with some other special cases.