메뉴 건너뛰기




Volumn 29, Issue 2, 2014, Pages 239-263

Augmented Lagrangian alternating direction method for matrix separation based on low-rank factorization

Author keywords

Alternating direction method; Augmented Lagrangian function; Matrix separation

Indexed keywords

ALTERNATING DIRECTION METHODS; AUGMENTED LAGRANGIAN FUNCTIONS; AUGMENTED LAGRANGIANS; DATA PREPROCESSING; FACTORIZATION MODEL; MATRIX SEPARATION; MINIMIZATION ALGORITHMS; SUITABLE CONDITIONS;

EID: 84888318611     PISSN: 10556788     EISSN: 10294937     Source Type: Journal    
DOI: 10.1080/10556788.2012.700713     Document Type: Article
Times cited : (239)

References (50)
  • 3
    • 77951291046 scopus 로고    scopus 로고
    • A singular value thresholding algorithm for matrix completion
    • J. Cai, E.J. Candès, and Z. Shen, A singular value thresholding algorithm for matrix completion, SIAM J. Optim. 20(4) (2010), pp. 1956-1982.
    • (2010) SIAM J. Optim. , vol.20 , Issue.4 , pp. 1956-1982
    • Cai, J.1    Candès, E.J.2    Shen, Z.3
  • 4
    • 71049116435 scopus 로고    scopus 로고
    • Exact matrix completion via convex optimization
    • E.J. Candès and B. Recht, Exact matrix completion via convex optimization, Found. Comput. Math. 9(6) (2009), pp. 717-772.
    • (2009) Found. Comput. Math. , vol.9 , Issue.6 , pp. 717-772
    • Candès, E.J.1    Recht, B.2
  • 5
    • 33744726904 scopus 로고    scopus 로고
    • Quantitative robust uncertainty principles and optimally sparse decompositions
    • E.J. Candès and J. Romberg, Quantitative robust uncertainty principles and optimally sparse decompositions, Found. Comput. Math. 6(2) (2006), pp. 227-254.
    • (2006) Found. Comput. Math. , vol.6 , Issue.2 , pp. 227-254
    • Candès, E.J.1    Romberg, J.2
  • 6
    • 33947416035 scopus 로고    scopus 로고
    • Near optimal signal recovery from random projections: Universal encoding strategies
    • E.J. Candès and T. Tao, Near optimal signal recovery from random projections: Universal encoding strategies, IEEE Trans. Inform. Theory 52(1) (2006), pp. 5406-5425.
    • (2006) IEEE Trans. Inform. Theory , vol.52 , Issue.1 , pp. 5406-5425
    • Candès, E.J.1    Tao, T.2
  • 7
    • 77951528523 scopus 로고    scopus 로고
    • The power of convex relaxation: Near-optimal matrix completion
    • E.J. Candès and T. Tao, The power of convex relaxation: Near-optimal matrix completion, IEEE Trans. Inform. Theory 56(5) (2010), pp. 2053-2080.
    • (2010) IEEE Trans. Inform. Theory , vol.56 , Issue.5 , pp. 2053-2080
    • Candès, E.J.1    Tao, T.2
  • 9
    • 31744440684 scopus 로고    scopus 로고
    • Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information
    • E.J. Candès, J. Romberg, and T. Tao, Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information, IEEE Trans. Inform. Theory 52 (2006), pp. 489-509.
    • (2006) IEEE Trans. Inform. Theory , vol.52 , pp. 489-509
    • Candès, E.J.1    Romberg, J.2    Tao, T.3
  • 12
    • 0002472542 scopus 로고
    • A proximal-based decomposition method for convex minimization problems
    • Ser. A
    • G. Chen and M. Teboulle, A proximal-based decomposition method for convex minimization problems, Math. Program. 64(1, Ser. A) (1994), pp. 81-101.
    • (1994) Math. Program. , vol.64 , Issue.1 , pp. 81-101
    • Chen, G.1    Teboulle, M.2
  • 13
    • 34548677063 scopus 로고    scopus 로고
    • Proximal thresholding algorithm for minimization over orthonormal bases
    • P.L. Combettes and J.-C. Pesquet, Proximal thresholding algorithm for minimization over orthonormal bases, SIAM J. Optim. 18(4) (2007), pp. 1351-1376.
    • (2007) SIAM J. Optim. , vol.18 , Issue.4 , pp. 1351-1376
    • Combettes, P.L.1    Pesquet, J.-C.2
  • 14
  • 16
    • 0027113845 scopus 로고
    • On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators
    • Ser. A
    • J. Eckstein and D.P. Bertsekas, On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators, Math. Program. 55(3, Ser. A) (1992), pp. 293-318.
    • (1992) Math. Program. , vol.55 , Issue.3 , pp. 293-318
    • Eckstein, J.1    Bertsekas, D.P.2
  • 17
    • 33947361050 scopus 로고    scopus 로고
    • Why simple shrinkage is still relevant for redundant representations?
    • M. Elad, Why simple shrinkage is still relevant for redundant representations? IEEE Trans. Inform. Theory 52(12) (2006), pp. 5559-5569.
    • (2006) IEEE Trans. Inform. Theory , vol.52 , Issue.12 , pp. 5559-5569
    • Elad, M.1
  • 19
    • 0142215333 scopus 로고    scopus 로고
    • Log-det heuristic for matrix rank minimization with applications to hankel and euclidean distance matrices
    • M. Fazel, H. Hindi, and S. Boyd, Log-det heuristic for matrix rank minimization with applications to hankel and euclidean distance matrices, Proceedings of the American Control Conference, 2003. Available at http://faculty.washington.edu/mfazel/acc03-final.pdf.
    • (2003) Proceedings of the American Control Conference
    • Fazel, M.1    Hindi, H.2    Boyd, S.3
  • 20
    • 0142200827 scopus 로고    scopus 로고
    • An em algorithm for wavelet-based image restoration
    • M. Figueiredo and R. Nowak, An EM algorithm for wavelet-based image restoration, IEEE Trans. Image Process. 12 (2003), pp. 906-916.
    • (2003) IEEE Trans. Image Process. , vol.12 , pp. 906-916
    • Figueiredo, M.1    Nowak, R.2
  • 21
    • 0003372342 scopus 로고
    • Augmented Lagrangian methods: Applications to the numerical solution of boundary value problems
    • North-Holland Publishing Co., Amsterdam, Translated from the French by B. Hunt and D. C. Spicer
    • M. Fortin and R. Glowinski, Augmented Lagrangian methods: Applications to the numerical solution of boundary value problems Vol. 15, in Studies in Mathematics and its Applications, North-Holland Publishing Co., Amsterdam, 1983. Translated from the French by B. Hunt and D. C. Spicer.
    • (1983) Studies in Mathematics and Its Applications , vol.15
    • Fortin, M.1    Glowinski, R.2
  • 25
    • 67349112355 scopus 로고    scopus 로고
    • Rank-constrained solutions to linear matrix equations using powerfactorization
    • J.P. Haldar and D. Hernando, Rank-constrained solutions to linear matrix equations using powerfactorization, IEEE Signal Process. Lett. 16 (2009), pp. 584-587.
    • (2009) IEEE Signal Process. Lett. , vol.16 , pp. 584-587
    • Haldar, J.P.1    Hernando, D.2
  • 26
    • 69649095451 scopus 로고    scopus 로고
    • Fixed-point continuation for l1-minimization: Methodology and convergence
    • E.T. Hale, W. Yin, and Y. Zhang, Fixed-point continuation for l1-minimization: Methodology and convergence, SIAM J. Optim. 19(3) (2008), pp. 1107-1130.
    • (2008) SIAM J. Optim. , vol.19 , Issue.3 , pp. 1107-1130
    • Hale, E.T.1    Yin, W.2    Zhang, Y.3
  • 27
    • 0242462717 scopus 로고    scopus 로고
    • A new inexact alternating directions method for monotone variational inequalities
    • Ser. A
    • B. He, L. Liao, D. Han, and H. Yang, A new inexact alternating directions method for monotone variational inequalities, Math. Program. 92(1, Ser. A) (2002), pp. 103-118.
    • (2002) Math. Program. , vol.92 , Issue.1 , pp. 103-118
    • He, B.1    Liao, L.2    Han, D.3    Yang, H.4
  • 28
    • 0034239566 scopus 로고    scopus 로고
    • Alternating direction method with self-adaptive penalty parameters for monotone variational inequalities
    • B. He, H. Yang, and S. Wang, Alternating direction method with self-adaptive penalty parameters for monotone variational inequalities, J. Optim. Theory Appl. 106(2) (2000), pp. 337-356.
    • (2000) J. Optim. Theory Appl. , vol.106 , Issue.2 , pp. 337-356
    • He, B.1    Yang, H.2    Wang, S.3
  • 29
    • 0034853839 scopus 로고    scopus 로고
    • A rank minimization heuristic with application to minimum order system approximation
    • H. Hindi M. Fazel, and S. Boyd, A rank minimization heuristic with application to minimum order system approximation, Proceedings American Control Conference 6, 2001, pp. 4734-4739.
    • (2001) Proceedings American Control Conference , vol.6 , pp. 4734-4739
    • Hindi, H.1    Fazel, M.2    Boyd, S.3
  • 30
    • 0033438023 scopus 로고    scopus 로고
    • Proximal decomposition via alternating linearization
    • K.C. Kiwiel, C.H. Rosa, and A. Ruszczyński, Proximal decomposition via alternating linearization, SIAM J. Optim. 9(3) (1999), pp. 668-689.
    • (1999) SIAM J. Optim. , vol.9 , Issue.3 , pp. 668-689
    • Kiwiel, K.C.1    Rosa, C.H.2    Ruszczyński, A.3
  • 31
    • 0002202679 scopus 로고    scopus 로고
    • A variable-penalty alternating directions method for convex optimization
    • Ser. A
    • S. Kontogiorgis and R.R. Meyer, A variable-penalty alternating directions method for convex optimization, Math. Program. 83(1, Ser. A) (1998), pp. 29-53.
    • (1998) Math. Program. , vol.83 , Issue.1 , pp. 29-53
    • Kontogiorgis, S.1    Meyer, R.R.2
  • 33
    • 7444243389 scopus 로고    scopus 로고
    • Statistical modeling of complex backgrounds for foreground object detection
    • L. Li, W. Huang, I. Gu, and Q. Tian, Statistical modeling of complex backgrounds for foreground object detection, IEEE Trans. Image Process. 13(11) (2004), pp. 1459-1472.
    • (2004) IEEE Trans. Image Process. , vol.13 , Issue.11 , pp. 1459-1472
    • Li, L.1    Huang, W.2    Gu, I.3    Tian, Q.4
  • 34
    • 80052482844 scopus 로고    scopus 로고
    • The augmented lagrange multiplier method for exact recovery of a corrupted low-rank matrices
    • (submitted)
    • Z. Lin, M. Chen, L. Wu, and Y. Ma, The augmented lagrange multiplier method for exact recovery of a corrupted low-rank matrices, Math. Program. (2009) (submitted).
    • (2009) Math. Program.
    • Lin, Z.1    Chen, M.2    Wu, L.3    Ma, Y.4
  • 38
    • 79957510064 scopus 로고    scopus 로고
    • Recovering low-rank and sparse components of matrices from incomplete and noisy observations
    • M. Tao and X. Yuan, Recovering low-rank and sparse components of matrices from incomplete and noisy observations, SIAM J. Optim. 21(1) (2011), pp. 57-81.
    • (2011) SIAM J. Optim. , vol.21 , Issue.1 , pp. 57-81
    • Tao, M.1    Yuan, X.2
  • 39
    • 0031285675 scopus 로고    scopus 로고
    • Alternating projection-proximal methods for convex programming and variational inequalities
    • P. Tseng, Alternating projection-proximal methods for convex programming and variational inequalities, SIAM J. Optim. 7(4) (1997), pp. 951-965.
    • (1997) SIAM J. Optim. , vol.7 , Issue.4 , pp. 951-965
    • Tseng, P.1
  • 40
    • 70049111607 scopus 로고    scopus 로고
    • On accelerated proximal gradient methods for convex-concave optimization
    • (submitted)
    • P. Tseng, On accelerated proximal gradient methods for convex-concave optimization, SIAM J. Optim. (2008) (submitted).
    • (2008) SIAM J. Optim.
    • Tseng, P.1
  • 41
    • 85012251675 scopus 로고    scopus 로고
    • A new alternating minimization algorithm for total variation image reconstruction
    • Y. Wang, J. Yang, W. Yin, and Y. Zhang, A new alternating minimization algorithm for total variation image reconstruction, SIAM J. Imaging Sci. 1(3) (2008), pp. 248-272.
    • (2008) SIAM J. Imaging Sci. , vol.1 , Issue.3 , pp. 248-272
    • Wang, Y.1    Yang, J.2    Yin, W.3    Zhang, Y.4
  • 44
    • 79952493979 scopus 로고    scopus 로고
    • Robust principal component analysis: Exact recovery of corrupted low-rank matrices by convex optimization
    • December
    • J. Wright, A. Ganesh, S. Rao, Y. Peng, and Y. Ma, Robust principal component analysis: Exact recovery of corrupted low-rank matrices by convex optimization, Proceedings of Neural Information Processing Systems (NIPS), December 2009. Available at https://netfiles.uiuc.edu/abalasu2/www/Files/ Wright09-NIPS.pdf.
    • (2009) Proceedings of Neural Information Processing Systems (NIPS)
    • Wright, J.1    Ganesh, A.2    Rao, S.3    Peng, Y.4    Ma, Y.5
  • 45
    • 77951137606 scopus 로고    scopus 로고
    • Robust principal component analysis: Exact recovery of corrupted low-rank matrices via convex optimization
    • (submitted)
    • J. Wright, A. Ganesh, S. Rao, Y. Peng, and Y. Ma, Robust principal component analysis: Exact recovery of corrupted low-rank matrices via convex optimization, J. ACM. (2009) (submitted).
    • (2009) J. ACM
    • Wright, J.1    Ganesh, A.2    Rao, S.3    Peng, Y.4    Ma, Y.5
  • 46
    • 76149100480 scopus 로고    scopus 로고
    • An efficient tvl1 algorithm for deblurring multichannel images corrupted by impulsive noise
    • J. Yang, Y. Zhang, and W. Yin, An efficient tvl1 algorithm for deblurring multichannel images corrupted by impulsive noise, SIAM J. Sci. Comput. 31(4) (2009), pp. 2842-2865.
    • (2009) SIAM J. Sci. Comput. , vol.31 , Issue.4 , pp. 2842-2865
    • Yang, J.1    Zhang, Y.2    Yin, W.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.