Smoothing fast proximal gradient algorithm for the relaxation of matrix rank regularization problem

This paper proposes a general inertial smoothing proximal gradient algorithm for solving the Capped-ℓ1 exact continuous relaxation regularization model proposed by Yu and Zhang (2022) [29]. The proposed algorithm incorporates different extrapolations into the gradient and proximal steps. It is prove...

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Bibliographic Details
Published in:Applied numerical mathematics Vol. 190; pp. 303 - 320
Main Authors: Zhang, Jie, Yang, Xinmin
Format: Journal Article
Language:English
Published: Elsevier B.V 01.08.2023
Subjects:
Convex nonsmooth loss function
Inertial proximal gradient algorithm
Matrix rank regularization problem
Smoothing approximation
Smoothing approximation
Inertial proximal gradient algorithm
Convex nonsmooth loss function
Matrix rank regularization problem
ISSN:0168-9274, 1873-5460
Online Access:Get full text
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Summary:This paper proposes a general inertial smoothing proximal gradient algorithm for solving the Capped-ℓ1 exact continuous relaxation regularization model proposed by Yu and Zhang (2022) [29]. The proposed algorithm incorporates different extrapolations into the gradient and proximal steps. It is proved that, under some general parameter constraints, the singular values of any accumulation point of the sequence generated by the proposed algorithm have the common support set, and the zero singular values can be achieved in a finite number of iterations. Furthermore, any accumulation point is a lifted stationary point of the relaxation model. Numerical experiments illustrate the efficiency of the proposed algorithm on synthetic and real data, respectively.
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2023.05.003