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Low-Rank Matrix Recovery Via Nonconvex Optimization Methods with Application to Errors-in-Variables Matrix Regression

Author

Listed:
  • Xin Li

    (Northwest University)

  • Dongya Wu

    (Northwest University)

Abstract

We consider the nonconvex regularized method for low-rank matrix recovery problems. Under suitable regularity conditions on the nonconvex loss function and the regularizer, we provide the recovery bound for any stationary point of the nonconvex method via separating singular values of the parameter matrix into larger and smaller ones. In this way, the established recovery bound can be much tighter than that of the convex nuclear norm regularized method when some of the singular values are larger than a threshold defined by the nonconvex regularizer. In addition, we consider the errors-in-variables matrix regression as an application of the nonconvex method. Probabilistic consequences and the advantage of the nonconvex method are demonstrated through verifying the regularity conditions for specific models with additive noise and missing data.

Suggested Citation

  • Xin Li & Dongya Wu, 2025. "Low-Rank Matrix Recovery Via Nonconvex Optimization Methods with Application to Errors-in-Variables Matrix Regression," Journal of Optimization Theory and Applications, Springer, vol. 205(3), pages 1-27, June.
    • Handle: RePEc:spr:joptap:v:205:y:2025:i:3:d:10.1007_s10957-025-02660-1
    DOI: 10.1007/s10957-025-02660-1
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