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

Ting Tao (), Shaohua Pan () and Shujun Bi ()
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Ting Tao: South China University of Technology
Shaohua Pan: South China University of Technology
Shujun Bi: South China University of Technology

Journal of Global Optimization, 2021, vol. 81, issue 4, No 7, 1017 pages

Abstract: 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.

Keywords: F-norm regularized factorization; Error bound; KL property of exponent 1/2 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10898-021-01077-0

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