Accelerated Line-search and Trust-region Methods

A line-search method, based on retractions, is formulated on Riemannian manifolds. This Riemannian line-search method, as well as a previouslyproposed Riemannian trust-region method, are further generalized to accelerated line-search and trust-region methods, where the next iterate is allowed to be any point that produces at least as much decrease in the cost function as a fixed fraction of the decrease produced by the proposed iterate. The global convergence of the methods is studied. Several occurences of these general algorithms exist in the literature and thus can benefit from our convergence analysis.