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Differential optimization in finite-dimensional spaces
On linear convergence of projected gradient method for a class of affine rank minimization problems
1. | School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China |
2. | Business School and China Academy of Corporate Governance, Nankai University, Tianjin 300071, China |
References:
[1] |
A. Beck and M. Teboulle, A linearly convergent algorithm for solving a class of nonconvex/affine feasibility problems,, In Fixed-Point Algorithms for Inverse Problems in Science and Engineering, 49 (2011), 33.
doi: 10.1007/978-1-4419-9569-8_3. |
[2] |
J.-F. Cai, E. J. Candès and Z. Shen, A singular value thresholding algorithm for matrix completion,, SIAM Journal on Optimization, 20 (2010), 1956.
doi: 10.1137/080738970. |
[3] |
E. J. Candès, X. Li, Y. Ma and J. Wright, Robust principal component analysis?,, Journal of the ACM (JACM), 58 (2011).
doi: 10.1145/1970392.1970395. |
[4] |
E. J. Candès and B. Recht, Exact matrix completion via convex optimization,, Foundations of Computational mathematics, 9 (2009), 717.
doi: 10.1007/s10208-009-9045-5. |
[5] |
M. Fazel, H. Hindi and S. P. Boyd, A rank minimization heuristic with application to minimum order system approximation,, In American Control Conference, 6 (2001), 4734.
doi: 10.1109/ACC.2001.945730. |
[6] |
D. Goldfarb and S. Ma, Convergence of fixed-point continuation algorithms for matrix rank minimization,, Foundations of Computational Mathematics, 11 (2011), 183.
doi: 10.1007/s10208-011-9084-6. |
[7] |
P. J. Huber, Robust statistics,, Springer, (2011). Google Scholar |
[8] |
P. Jain, R. Meka and I. S. Dhillon, Guaranteed rank minimization via singular value projection,, In NIPS, 23 (2010), 937. Google Scholar |
[9] |
L. Kong, J. Sun and N. Xiu, S-semigoodness for low-rank semidefinite matrix recovery,, Pacific Journal of Optimization, 10 (2014), 73.
|
[10] |
L. Kong, J. Sun, J. Tao and N. Xiu, Sparse recovery on Euclidean Jordan algebras,, Linear Algebra and Applications, 465 (2015), 65.
doi: 10.1016/j.laa.2014.09.018. |
[11] |
Z. Lin, M. Chen and Y. Ma, The augmented lagrange multiplier method for exact recovery of corrupted low-rank matrices,, , (2010). Google Scholar |
[12] |
N. Linial, E. London and Y. Rabinovich, The geometry of graphs and some of its algorithmic applications,, Combinatorica, 15 (1995), 215.
doi: 10.1007/BF01200757. |
[13] |
Z. Liu and L. Vandenberghe, Interior-point method for nuclear norm approximation with application to system identification,, SIAM Journal on Matrix Analysis and Applications, 31 (2009), 1235.
doi: 10.1137/090755436. |
[14] |
N. Natarajan and I. S. Dhillon, Inductive matrix completion for predicting gene-disease associations,, Bioinformatics, 30 (2014).
doi: 10.1093/bioinformatics/btu269. |
[15] |
B. Recht, M. Fazel and P. A. Parrilo, Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization,, SIAM Review, 52 (2010), 471.
doi: 10.1137/070697835. |
[16] |
K.-C. Toh and S. Yun, An accelerated proximal gradient algorithm for nuclear norm regularized linear least squares problems,, Pacific Journal of Optimization, 6 (2010), 615.
|
[17] |
X. Yuan and J. Yang, Sparse and low-rank matrix decomposition via alternating direction methods,, Pac. J. Optim., 9 (2013), 167.
|
[18] |
S. Zhang, J. Ang and J. Sun, An alternating direction method for solving convex nonlinear semidefinite programming problems,, Optimization, 62 (2013), 527.
doi: 10.1080/02331934.2011.611883. |
show all references
References:
[1] |
A. Beck and M. Teboulle, A linearly convergent algorithm for solving a class of nonconvex/affine feasibility problems,, In Fixed-Point Algorithms for Inverse Problems in Science and Engineering, 49 (2011), 33.
doi: 10.1007/978-1-4419-9569-8_3. |
[2] |
J.-F. Cai, E. J. Candès and Z. Shen, A singular value thresholding algorithm for matrix completion,, SIAM Journal on Optimization, 20 (2010), 1956.
doi: 10.1137/080738970. |
[3] |
E. J. Candès, X. Li, Y. Ma and J. Wright, Robust principal component analysis?,, Journal of the ACM (JACM), 58 (2011).
doi: 10.1145/1970392.1970395. |
[4] |
E. J. Candès and B. Recht, Exact matrix completion via convex optimization,, Foundations of Computational mathematics, 9 (2009), 717.
doi: 10.1007/s10208-009-9045-5. |
[5] |
M. Fazel, H. Hindi and S. P. Boyd, A rank minimization heuristic with application to minimum order system approximation,, In American Control Conference, 6 (2001), 4734.
doi: 10.1109/ACC.2001.945730. |
[6] |
D. Goldfarb and S. Ma, Convergence of fixed-point continuation algorithms for matrix rank minimization,, Foundations of Computational Mathematics, 11 (2011), 183.
doi: 10.1007/s10208-011-9084-6. |
[7] |
P. J. Huber, Robust statistics,, Springer, (2011). Google Scholar |
[8] |
P. Jain, R. Meka and I. S. Dhillon, Guaranteed rank minimization via singular value projection,, In NIPS, 23 (2010), 937. Google Scholar |
[9] |
L. Kong, J. Sun and N. Xiu, S-semigoodness for low-rank semidefinite matrix recovery,, Pacific Journal of Optimization, 10 (2014), 73.
|
[10] |
L. Kong, J. Sun, J. Tao and N. Xiu, Sparse recovery on Euclidean Jordan algebras,, Linear Algebra and Applications, 465 (2015), 65.
doi: 10.1016/j.laa.2014.09.018. |
[11] |
Z. Lin, M. Chen and Y. Ma, The augmented lagrange multiplier method for exact recovery of corrupted low-rank matrices,, , (2010). Google Scholar |
[12] |
N. Linial, E. London and Y. Rabinovich, The geometry of graphs and some of its algorithmic applications,, Combinatorica, 15 (1995), 215.
doi: 10.1007/BF01200757. |
[13] |
Z. Liu and L. Vandenberghe, Interior-point method for nuclear norm approximation with application to system identification,, SIAM Journal on Matrix Analysis and Applications, 31 (2009), 1235.
doi: 10.1137/090755436. |
[14] |
N. Natarajan and I. S. Dhillon, Inductive matrix completion for predicting gene-disease associations,, Bioinformatics, 30 (2014).
doi: 10.1093/bioinformatics/btu269. |
[15] |
B. Recht, M. Fazel and P. A. Parrilo, Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization,, SIAM Review, 52 (2010), 471.
doi: 10.1137/070697835. |
[16] |
K.-C. Toh and S. Yun, An accelerated proximal gradient algorithm for nuclear norm regularized linear least squares problems,, Pacific Journal of Optimization, 6 (2010), 615.
|
[17] |
X. Yuan and J. Yang, Sparse and low-rank matrix decomposition via alternating direction methods,, Pac. J. Optim., 9 (2013), 167.
|
[18] |
S. Zhang, J. Ang and J. Sun, An alternating direction method for solving convex nonlinear semidefinite programming problems,, Optimization, 62 (2013), 527.
doi: 10.1080/02331934.2011.611883. |
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