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Error bound of critical points and KL property of exponent 1/2 for squared F-norm regularized factorization

Author

Listed:
  • Ting Tao

    (South China University of Technology)

  • Shaohua Pan

    (South China University of Technology)

  • Shujun Bi

    (South China University of Technology)

Abstract

This paper is concerned with the squared F(robenius)-norm regularized factorization form for noisy low-rank matrix recovery problems. Under a suitable assumption on the restricted condition number of the Hessian matrix of the loss function, we establish an error bound to the true matrix for the non-strict critical points with rank not more than that of the true matrix. Then, for the squared F-norm regularized factorized least squares loss function, we establish its KL property of exponent 1/2 on the global optimal solution set under the noisy and full sample setting, and achieve this property at its certain class of critical points under the noisy and partial sample setting. These theoretical findings are also confirmed by solving the squared F-norm regularized factorization problem with an accelerated alternating minimization method.

Suggested Citation

  • Ting Tao & Shaohua Pan & Shujun Bi, 2021. "Error bound of critical points and KL property of exponent 1/2 for squared F-norm regularized factorization," Journal of Global Optimization, Springer, vol. 81(4), pages 991-1017, December.
    • Handle: RePEc:spr:jglopt:v:81:y:2021:i:4:d:10.1007_s10898-021-01077-0
    DOI: 10.1007/s10898-021-01077-0
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    References listed on IDEAS

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    1. Hédy Attouch & Jérôme Bolte & Patrick Redont & Antoine Soubeyran, 2010. "Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Łojasiewicz Inequality," Mathematics of Operations Research, INFORMS, vol. 35(2), pages 438-457, May.
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