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arXiv · 2312.01014

Generalized Left-Localized Cayley Parametrization for Optimization with Orthogonality Constraints

Kieta Kume·Isao Yamada
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Abstract

We present a reformulation of optimization problems over the Stiefel manifold by using a Cayley-type transform, named the generalized left-localized Cayley transform, for the Stiefel manifold. The reformulated optimization problem is defined over a vector space, whereby we can apply directly powerful computational arts designed for optimization over a vector space. The proposed Cayley-type transform enjoys several key properties which are useful to (i) study relations between the original problem and the proposed problem; (ii) check the conditions to guarantee the global convergence of optimization algorithms. Numerical experiments demonstrate that the proposed algorithm outperforms the standard algorithms designed with a retraction on the Stiefel manifold.

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Kieta Kume, Isao Yamada. 2023-12-02. Generalized Left-Localized Cayley Parametrization for Optimization with Orthogonality Constraints. https://doi.org/10.1080/02331934.2022.2142471

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