EXPANDING THE APPLICABILITY OF THE GAUSS-NEWTON METHOD FOR CONVEX OPTIMIZATION UNDER RESTRICTED CONVERGENCE DOMAINS AND MAJORANT CONDITIONS

Abstract

Using 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.