AM  Vol.5 No.21 , December 2014
On Accelerated Singular Value Thresholding Algorithm for Matrix Completion
ABSTRACT
An accelerated singular value thresholding (SVT) algorithm was introduced for matrix completion in a recent paper [1], which applies an adaptive line search scheme and improves the convergence rate from O(1/N) for SVT to O(1/N2), where N is the number of iterations. In this paper, we show that it is the same as the Nemirovski’s approach, and then modify it to obtain an accelerate Nemirovski’s technique and prove the convergence. Our preliminary computational results are very favorable.

Cite this paper
Wang, L. , Hu, J. and Chen, C. (2014) On Accelerated Singular Value Thresholding Algorithm for Matrix Completion. Applied Mathematics, 5, 3445-3451. doi: 10.4236/am.2014.521322.
References
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http://dx.doi.org/10.1145/2339530.2339581

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[6]   Cai, J.F., Candès, E.J. and Shen, Z. (2010) A Singular Value Thresholding Algorithm for Matrix Completion. SIAM Journal on Optimization, 20, 1956-1982.
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[7]   Toh, K.C. and Yun, S. (2010) An Accelerated Proximal Gradient Algorithm for Nuclear Norm Regularized Least Squares Problems. Pacific Journal of Optimization, 6, 615-640.

[8]   Nemirovski, A. (1994) Lecture Notes on Efficient Methods in Convex Programming.
http://www2.isye.gatech.edu/~nemirovs/Lect_EMCO.pdf

[9]   Liu, J., Chen, J. and Ye, J. (2009) Large-Scale Sparse Logistic Regression. Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Paris, 28 June-1 July 2009, 547-556.
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[10]   Nesterov, Y. (2003) Introductory Lectures on Convex Optimization: A Basic Course. Kluwer Academic Publishers, Norwell.

 
 
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