IEEE Access (Jan 2024)

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

  • Keita Kume,
  • Isao Yamada

DOI
https://doi.org/10.1109/ACCESS.2024.3368631
Journal volume & issue
Vol. 12
pp. 31312 – 31323

Abstract

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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