A Non-monotone Linear Search Method with Mixed Direction on Stiefel Manifold

Abstract: 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.