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An improved Riemannian conjugate gradient method and its application to robust matrix completion

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Abstract

This paper presents a new conjugate gradient method on Riemannian manifolds and establishes its global convergence under the standard Wolfe line search. The proposed algorithm is a generalization of a Wei-Yao-Liu-type Hestenes-Stiefel method from Euclidean space to the Riemannian setting. We prove that the new algorithm is well-defined, generates a descent direction at each iteration, and globally converges when the step lengths satisfy the standard Wolfe conditions. Numerical experiments on the matrix completion problem demonstrate the efficiency of the proposed method.

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The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

We would like to express our appreciation to the editor and an anonymous referee for providing valuable feedback that improved the quality of this paper.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran

    Shahabeddin Najafi & Masoud Hajarian

Authors
  1. Shahabeddin Najafi
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  2. Masoud Hajarian
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Contributions

SN: software, validation, formal analysis, writing—original draft, investigation, conceptualization, methodology. MH: writing—review and editing, supervision.

Corresponding author

Correspondence to Masoud Hajarian.

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Najafi, S., Hajarian, M. An improved Riemannian conjugate gradient method and its application to robust matrix completion. Numer Algor 96, 1887–1900 (2024). https://doi.org/10.1007/s11075-023-01688-6

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  • DOI: https://doi.org/10.1007/s11075-023-01688-6

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