Projected nonmonotone search methods for optimization with orthogonality constraints

In this paper, we propose two feasible methods based on projections using a curvilinear search for solving optimization problems with orthogonality constraints. In one of them we apply a projected Adams–Moulton-like update scheme. All our algorithms compute the SVD decomposition in each iteration to preserve feasibility. Additionally, we present some convergence results. Finally, we perform numerical experiments with simulated problems; and analyze the performance of the proposed methods compared with state-of-the-art algorithms.