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

Xin Li () and Dongya Wu ()
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Xin Li: Northwest University
Dongya Wu: Northwest University

Journal of Optimization Theory and Applications, 2025, vol. 205, issue 3, No 1, 27 pages

Abstract: 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.

Keywords: Low-rank matrix recovery; Nonconvex optimization; Nonconvex regularization; Recovery bounds; Errors-in-variables matrix regression; 90C26; 90C30; 62F30 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02660-1

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