-

 

 

 




Optimization Online





 

Solving A Low-Rank Factorization Model for Matrix Completion by A Nonlinear Successive Over-Relaxation Algorithm

Zaiwen Wen(zw2109***at***columbia.edu)
Wotao Yin(wotao.yin***at***rice.edu)
Yin Zhang(yzhang***at***rice.edu)

Abstract: 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 nuclear-norm 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. Convergence of this nonlinear SOR algorithm is analyzed. Numerical results 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.

Keywords: Matrix Completion, alternating minimization, nonlinear GS method, nonlinear SOR method

Category 1: Nonlinear Optimization

Category 2: Applications -- Science and Engineering

Citation: @TECHREPORT{LMaFit:report, author = {Wen, Zaiwen and Yin, Wotao and Zhang, Yin}, title = {Solving A Low-Rank Factorization Model for Matrix Completion by A Nonlinear Successive Over-Relaxation Algorithm}, institution = {Rice University}, year = {2010}, note = {CAAM Technical Report TR10-07} }

Download: [PDF]

Entry Submitted: 03/26/2010
Entry Accepted: 03/26/2010
Entry Last Modified: 03/26/2010

Modify/Update this entry


  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository

 

Submit
Update
Policies
Coordinator's Board
Classification Scheme
Credits
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Programming Society