Extending the applicability of Gauss-Newton method for convex composite optimization on Riemannian manifolds

We present a semi-local convergence analysis of the Gauss-Newton method for solving convex composite optimization problems in Riemannian manifolds using the notion of quasi-regularity for an initial point. Using a combination the L-average Lipszhitz condition and the center L0-average Lipschitz condition we introduce majorizing sequences for the Gauss-Newton method that are more precise than in earlier studies. Consequently, our semi-local convergence analysis for the Gauss-Newton method has the following advantages under the same computational cost: weaker sufficient convergence conditions; more precise estimates on the distances involved and an at least as precise information on the location of the solution.