Local convergence analysis of inexact Gauss–Newton method for singular systems of equations under majorant and center-majorant condition

We present a new semi-local convergence analysis of the Gauss–Newton method for solving convex composite optimization problems using the concept of quasi-regularity for an initial point. The convergence analysis is based on a combination of a center-majorant and a majorant function. 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 more precise and the convergence ball is at least as large. Numerical examples are also provided in this study. © 2015, Sociedad Española de Matemática Aplicada.