A randomized feasible algorithm for optimization with orthogonal constraints

Fan Fei (), Yuchen Feng () and Jinyan Fan ()
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Fan Fei: Shanghai Jiao Tong University
Yuchen Feng: Shanghai Jiao Tong University
Jinyan Fan: Shanghai Jiao Tong University

Computational Optimization and Applications, 2025, vol. 92, issue 1, No 1, 27 pages

Abstract: Abstract In this paper, we propose a randomized feasible algorithm for optimization over the Stiefel manifold, where only some randomly chosen columns of the variable matrix are updated at each iteration. It is proved that the sequence of Riemannian gradients generated by the algorithm converges to zero with probability one. Numerical results show that the algorithm is efficient, especially for the problems when the matrices involved are sparse.

Keywords: Optimization over the Stiefel manifold; Randomized feasible algorithm; Cayley transformation; Almost-sure global convergence; 49Q99; 65K05; 90C26; 90C30 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10589-025-00693-w

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