Journal
MATHEMATICAL PROGRAMMING COMPUTATION
Volume 4, Issue 4, Pages 333-361Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s12532-012-0044-1
Keywords
Matrix completion; Alternating minimization; Nonlinear GS method; Nonlinear SOR method
Categories
Funding
- NSF through UCLA IPAM [DMS-0439872]
- NSFC [11101274]
- NSF CAREER Award [DMS-07-48839]
- ONR [N00014-08-1-1101]
- Alfred P. Sloan Research Fellowship
- NSF [DMS-0405831, DMS-0811188]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1115950] Funding Source: National Science Foundation
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The matrix completion problem is to recover a low-rank matrix from a subset of its entries. The main solution strategy for this problem has been based on nuclearnorm minimization which requires computing singular value decompositions-a task that is increasingly costly as matrix sizes and ranks increase. To improve the capacity of solving large-scale problems, we propose a low-rank factorization model and construct a nonlinear successive over-relaxation (SOR) algorithm that only requires solving a linear least squares problem per iteration. Extensive numerical experiments show that the algorithm can reliably solve a wide range of problems at a speed at least several times faster than many nuclear-norm minimization algorithms. In addition, convergence of this nonlinear SOR algorithm to a stationary point is analyzed.
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