Proximal Quasi-Newton Method for Composite Optimization over the Stiefel Manifold.

In this paper, we consider the composite optimization problems over the Stiefel manifold. A successful method to solve this class of problems is the proximal gradient method proposed by Chen et al. (SIAM J Optim 30:210–239, 2020. https://doi.org/10.1137/18M122457X). Motivated by the proximal Newton-type techniques in the Euclidean space, we present a Riemannian proximal quasi-Newton method, named ManPQN, to solve the composite optimization problems. The global convergence of the ManPQN method is proved and iteration complexity for obtaining an ϵ -stationary point is analyzed. Under some mild conditions, we also establish the local linear convergence result of the ManPQN method. Numerical results are encouraging, which shows that the proximal quasi-Newton technique can be used to accelerate the proximal gradient method. [ABSTRACT FROM AUTHOR]