Adaptive Localized Cayley Parametrization for Optimization Over Stiefel Manifold and Its Convergence Rate Analysis

Abstract

The Adaptive Localized Cayley Parametrization (ALCP) strategy for orthogonality constrained optimization has been proposed as a scheme to utilize Euclidean optimization algorithms on an adaptive parametrization of the Stiefel manifold via a tunable generalized left-localized Cayley parametrization. Thanks to the adaptive parametrization, the ALCP strategy enjoys stable convergence of the estimate sequence of a minimizer by avoiding a certain singular-point issue. In this paper, we present a convergence rate analysis for the ALCP strategy using Euclidean optimization algorithms such as Nesterov-type accelerated gradient methods. Numerical experiments demonstrate the effectiveness of the ALCP strategy.

Keywords

• Nonconvex optimization
• orthogonality constraints
• Stiefel manifold
• generalized leftlocalized Cayley transform
• convergence rate analysis