A Nesterov-type Acceleration with Adaptive Localized Cayley Parametrization for Optimization over the Stiefel Manifold

Abstract

Despite certain singular-point issues, the Cayley parametrization (CP) has great potential to serve as a key to import many powerful strategies, developed originally for optimization over a vector space, into the task for optimization over the Stiefel manifold. In this paper, we newly present (i) a computationally efficient CP that can circumvent the singularpoint issues and (ii) a Nesterov type accelerated gradient method, based on the proposed CP, with its convergence analysis. To guarantee the convergence, we also evaluate a Lipschitz constant of the gradient of the cost function in the CP domain. Numerical experiments show excellent performance of the proposed accelerated algorithm compared with the standard algorithms, e.g., the Barzilai-Borwein method and L-BFGS method, combined with a vector transport for optimization over the Stiefel manifold as a special instance of the Riemannian manifold.