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- Title
Nonconvex mixed matrix minimization.
- Authors
Meijuan Shang; Yanan Liu; Lingchen Kong; Xianchao Xiu; Ying Yang
- Abstract
Given the ultrahigh dimensionality and the complex structure, which contains matrices and vectors, the mixed matrix minimization becomes crucial for the analysis of those data. Recently, the nonconvex functions such as the smoothly clipped absolute deviation, the minimax concave penalty, the capped l1-norm penalty and the lp quasi-norm with 0 < p < 1 have been shown remarkable advantages in variable selection due to the fact that they can overcome the over-penalization. In this paper, we propose and study a novel nonconvex mixed matrix minimization, which combines the low-rank and sparse regularzations and nonconvex functions perfectly. The augmented Lagrangian method (ALM) is proposed to solve the noncovnex mixed matrix minimization problem. The resulting subproblems either have closed-form solutions or can be solved by fast solvers, which makes the ALM particularly efficient. In theory, we prove that the sequence generated by the ALM converges to a stationary point when the penalty parameter is above a computable threshold. Extensive numerical experiments illustrate that our proposed nonconvex mixed matrix minimization model outperforms the existing ones.
- Subjects
DIMENSION reduction (Statistics); MATRICES (Mathematics); DATA analysis; TECHNOLOGY convergence
- Publication
Mathematical Foundations of Computing, 2019, Vol 2, Issue 2, p107
- ISSN
2577-8838
- Publication type
Article
- DOI
10.3934/mfc.2019009