Extended Gauss-Newton Method on Riemannian Manifolds for Convex Composite Optimization Problems

Abstract

The Gauss-Newton method has been used to generate a sequence to approximate a zero of a vector field defined on a Riemannian manifold. The sufficient convergence conditions are based on L-average continuity conditions on the covariant derivative. In this work, the convergence conditions are weakened with advantages: tighter error distances and more precise information about the zero. These improvements are realized since tighter majorizing sequences are generated than in earlier studies. The scalar functions controlling the derivative are at least as tight as the specializations of earlier ones. Therefore, the new results are obtained without additional computational effort. Numerical applications are utilized to verify the convergence conditions.