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Title
Japanese: 
English:Generalized left-localized Cayley parametrization for optimization with orthogonality constraints 
Author
Japanese: 久米 啓太, 山田 功.  
English: Keita Kume, Isao Yamada.  
Language English 
Journal/Book name
Japanese: 
English:Optimization 
Volume, Number, Page        
Published date Nov. 15, 2022 
Publisher
Japanese: 
English: 
Conference name
Japanese: 
English: 
Conference site
Japanese: 
English: 
DOI https://doi.org/10.1080/02331934.2022.2142471
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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