IEEE Access (Jan 2024)
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.
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