Convergence of the Gauss-Newton method for convex composite optimization   under a majorant condition
  Under the hypothesis that an initial point is a quasi-regular point, we use a majorant condition to present a new semi-local convergence analysis of an extension of the Gauss-Newton method for solving convex composite optimization problems. In this analysis the conditions and proof of convergence are simplified by using a simple majorant condition to define regions where a Gauss-Newton sequence is "well behaved". 
Orizon Perreira Ferreira, Max Leandro Nobre Gon\c{c}alves, Paulo   Roberto Oliveira
math.OC