Gauss–Newton method for convex composite optimizations on Riemannian manifolds

A notion of quasi‐regularity is extended for the inclusion problem $F(p)\in C$ , where F is a differentiable mapping from a Riemannian manifold M to ${ℝ}^n$ . When C is the set of minimum points of a convex real‐valued function h on ${ℝ}^n$ and DF satisfies the L‐average Lipschitz condition, we use the majorizing function technique to establish the semi‐local convergence of sequences generated by the Gauss‐Newton method (with quasi‐regular initial points) for the convex composite function h ∘ F on Riemannian manifold. Two applications are provided: one is for the case of regularities on Riemannian manifolds and the other is for the case when C is a cone and DF(p 0)(·) - C is surjective. In particular, the results obtained in this paper extend the corresponding one in Wang et al. (2009).