# Two-Step Proximal Gradient Algorithm for Low-Rank Matrix Completion

### Abstract

In this paper, we propose a two-step proximal gradient algorithm to solve nuclear norm regularized least squares for the purpose of recovering low-rank data matrix from sampling of its entries. Each iteration generated by the proposed algorithm is a combination of the latest three points, namely, the previous point, the current iterate, and its proximal gradient point. This algorithm preserves the computational simplicity of classical proximal gradient algorithm where a singular value decomposition in proximal operator is involved. Global convergence is followed directly in the literature. Numerical results are reported to show the efficiency of the algorithm.### References

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*Statistics, Optimization & Information Computing*,

*4*(2), 174-182. https://doi.org/10.19139/soic.v4i2.201

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