  In this paper, we propose a non-monotone line search method for solving
optimization problems on Stiefel manifold. Our method uses as a search
direction a mixed gradient based on a descent direction, and a Barzilai-Borwein
line search. Feasibility is guaranteed by projecting each iterate on the
Stiefel manifold, through SVD factorizations. Some theoretical results for
analyzing the algorithm are presented. Finally, we provide numerical
experiments comparing our algorithm with other state-of-the-art procedures.
