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Convergence analysis of projected gradient descent for Schatten-p nonconvex matrix recovery

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Abstract

The matrix rank minimization problem arises in many engineering applications. As this problem is NP-hard, a nonconvex relaxation of matrix rank minimization, called the Schatten-p quasi-norm minimization (0 < p < 1), has been developed to approximate the rank function closely. We study the performance of projected gradient descent algorithm for solving the Schatten-p quasi-norm minimization (0 < p < 1) problem. Based on the matrix restricted isometry property (M-RIP), we give the convergence guarantee and error bound for this algorithm and show that the algorithm is robust to noise with an exponential convergence rate.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China

    Yun Cai & Song Li

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  1. Yun Cai
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  2. Song Li
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Correspondence to Song Li.

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Cai, Y., Li, S. Convergence analysis of projected gradient descent for Schatten-p nonconvex matrix recovery. Sci. China Math. 58, 845–858 (2015). https://doi.org/10.1007/s11425-014-4949-1

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  • DOI: https://doi.org/10.1007/s11425-014-4949-1

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