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<p>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.</p>

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A randomized feasible algorithm for optimization with orthogonal constraints

  • 期刊论文

  • 发表日期：

    2025年5月22日

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  • Fan Fei,
  • Yuchen Feng,
  • Jinyan Fan

摘要

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.