Expanding the applicability of the Gauss–Newton method for convex optimization under a majorant condition

Abstract

A new semi-local convergence analysis of the Gauss–Newton method for solving convex composite optimization problems is presented using the concept of quasi-regularity for an initial point. Our 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 using a majorant function or Wang’s condition or Lipchitz condition. The special cases and applications include regular starting points, Robinson’s conditions, Smale’s or Wang’s theory.