Argyros, I.K.George, S.2020-03-312020-03-312017Nonlinear Functional Analysis and Applications, 2017, Vol.22, 1, pp.197-207https://idr.nitk.ac.in/handle/123456789/11119Using our new idea of restricted convergent domains, new semi-local convergence analysis of the Gauss-Newton method for solving convex composite optimization problems is presented. Our convergence analysis is based on a combination of a center-majorant and 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. 2017 Kyungnam University Press.Article