Argyros, I.K.George, S.2026-02-052017Nonlinear Functional Analysis and Applications, 2017, 22, 1, pp. 197-20712291595https://idr.nitk.ac.in/handle/123456789/25665Using 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.Center-majorant functionConvex composite optimization problemGauss-Newton methodMajorant functionRestricted convergeny domainsSemi-local convergence