Extended local convergence analysis of inexact Gauss-Newton method for singular systems of equations under weak conditions

Abstract

A new semi-local convergence analysis of the Gauss-Newton method for solving convex composite optimization problems is presented using restricted convergence domains. The results extend the applicability of the Gauss-Newton method under the same computational cost as in earlier studies. In particular, the advantages are: the error estimates on the distances involved are tighter and the convergence ball is at least as large. Moreover, the majorant function in contrast to earlier studies is not necessarily differentiable. Numerical examples are also provided in this study.