A Riemannian rank-adaptive method for low-rank optimization

  • Pierre-Antoine Absil
  • Kyle A. Gallivan
  • Wen Huang
  • Paul Van Dooren
  • Guifang Zhou
    • Categories Constrained Nonlinear Optimization, Data-Mining Short URL: https://optimization-online.org/?p=13817

    This paper presents an algorithm that solves optimization problems on a matrix manifold $\mathcal{M} \subseteq \mathbb{R}^{m \times n}$ with an additional rank inequality constraint. The algorithm resorts to well-known Riemannian optimization schemes on fixed-rank manifolds, combined with new mechanisms to increase or decrease the rank. The convergence of the algorithm is analyzed and a weighted low-rank approximation problem is used to illustrate the efficiency and effectiveness of the algorithm.

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    Technical report UCL-INMA-2015.05

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