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Affine matrix rank minimization problem via non-convex fraction function penalty.
- Source :
-
Journal of Computational & Applied Mathematics . Jul2018, Vol. 336, p353-374. 22p. - Publication Year :
- 2018
-
Abstract
- Affine matrix rank minimization problem is a fundamental problem in many important applications. It is well known that this problem is combinatorial and NP-hard in general. In this paper, a continuous promoting low rank non-convex fraction function is studied to replace the rank function in this NP-hard problem. An iterative singular value thresholding algorithm is proposed to solve the regularization transformed affine matrix rank minimization problem. With the change of the parameter in non-convex fraction function, we could get some much better results, which is one of the advantages for the iterative singular value thresholding algorithm compared with some state-of-art methods. Some convergence results are established. Moreover, we proved that the value of the regularization parameter λ > 0 cannot be chosen too large. Indeed, there exists λ ̄ > 0 such that the optimal solution of the regularization transformed affine matrix rank minimization problem is equal to zero for any λ > λ ̄ . Numerical experiments on matrix completion problems and image inpainting problems show that our method performs effective in finding a low-rank matrix compared with some state-of-art methods. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03770427
- Volume :
- 336
- Database :
- Academic Search Index
- Journal :
- Journal of Computational & Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 127842512
- Full Text :
- https://doi.org/10.1016/j.cam.2017.12.048