Gauss-Newton method for convex composite optimizations on Riemannian manifolds

摘要

A notion of quasi-regularity is extended for the inclusion problem F(p) e 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 o 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(Po)(·) - C is surjective. In particular, the results obtained in this paper extend the corresponding one in Wang et al. (Taiwanese J Math 13:633-656,2009).