Simple Acceleration of the Riemannian Steepest Descent Method with the Armijo Condition

This paper proposes a novel modification of the Riemannian steepest descent (R-SD) method with the Armijo backtracking line search. Although the proposed approach is simple because it only modifies the step lengths satisfying the Armijo condition, the results of the numerical experiments show that the approach significantly improves the performance of the standard R-SD method. Furthermore, it can be guaranteed that the global convergence and locally linear convergence properties of the original standard R-SD method are maintained in the proposed method.