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Volumn 155, Issue 1, 2012, Pages 227-238

A Note on the Alternating Direction Method of Multipliers

Author keywords

Alternating direction method of multipliers; Global convergence; Strongly convex functions

Indexed keywords

FUNCTIONS;

EID: 84867535196     PISSN: 00223239     EISSN: 15732878     Source Type: Journal    
DOI: 10.1007/s10957-012-0003-z     Document Type: Article
Times cited : (191)

References (26)
  • 1
    • 0002211517 scopus 로고
    • A dual algorithm for the solution of nonlinear variational problems via finite element approximations
    • Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximations. Comput. Math. Appl. 2, 17-40 (1976).
    • (1976) Comput. Math. Appl. , vol.2 , pp. 17-40
    • Gabay, D.1    Mercier, B.2
  • 2
    • 77957064934 scopus 로고
    • Applications of the method of multipliers to variational inequalities
    • M. Fortin and R. Glowinski (Eds.), Amsterdam: North-Holland
    • Gabay, D.: Applications of the method of multipliers to variational inequalities. In: Fortin, M., Glowinski, R. (eds.) Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary-Value Problems, pp. 299-331. North-Holland, Amsterdam (1983).
    • (1983) Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary-Value Problems , pp. 299-331
    • Gabay, D.1
  • 3
    • 0002472542 scopus 로고
    • A proximal-based decomposition method for convex minimization problems
    • Chen, G., Teboulle, M.: A proximal-based decomposition method for convex minimization problems. Math. Program. 64, 81-101 (1994).
    • (1994) Math. Program. , vol.64 , pp. 81-101
    • Chen, G.1    Teboulle, M.2
  • 4
    • 0027113845 scopus 로고
    • On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators
    • Eckstein, J., Bertsekas, D. P.: On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators. Math. Program. 55, 293-318 (1992).
    • (1992) Math. Program. , vol.55 , pp. 293-318
    • Eckstein, J.1    Bertsekas, D.P.2
  • 5
    • 0002788352 scopus 로고
    • Application of the alternating directions method of multipliers to separable convex programming problems
    • Fukushima, M.: Application of the alternating directions method of multipliers to separable convex programming problems. Comput. Optim. Appl. 2, 93-111 (1992).
    • (1992) Comput. Optim. Appl. , vol.2 , pp. 93-111
    • Fukushima, M.1
  • 6
    • 0242462717 scopus 로고    scopus 로고
    • A new inexact alternating direction method for monotone variational inequalities
    • He, B. S., Liao, L. Z., Han, D. R., Yang, H.: A new inexact alternating direction method for monotone variational inequalities. Math. Program. 92, 103-118 (2002).
    • (2002) Math. Program. , vol.92 , pp. 103-118
    • He, B.S.1    Liao, L.Z.2    Han, D.R.3    Yang, H.4
  • 7
    • 0002202679 scopus 로고    scopus 로고
    • A variable-penalty alternating directions method for convex optimization
    • Kontogiorgis, S., Meyer, R. R.: A variable-penalty alternating directions method for convex optimization. Math. Program. 83, 29-53 (1998).
    • (1998) Math. Program. , vol.83 , pp. 29-53
    • Kontogiorgis, S.1    Meyer, R.R.2
  • 8
    • 0026077016 scopus 로고
    • Applications of a splitting algorithm to decomposition in convex programming and variational inequalities
    • Tseng, P.: Applications of a splitting algorithm to decomposition in convex programming and variational inequalities. SIAM J. Control Optim. 29, 119-138 (1991).
    • (1991) SIAM J. Control Optim. , vol.29 , pp. 119-138
    • Tseng, P.1
  • 9
    • 80052894191 scopus 로고    scopus 로고
    • Alternating direction method for image inpainting in wavelet domain
    • Chan, R. H., Yang, J. F., Yuan, X. M.: Alternating direction method for image inpainting in wavelet domain. SIAM J. Imaging Sci. 4, 807-826 (2011).
    • (2011) SIAM J. Imaging Sci. , vol.4 , pp. 807-826
    • Chan, R.H.1    Yang, J.F.2    Yuan, X.M.3
  • 10
    • 84863068818 scopus 로고    scopus 로고
    • Matrix completion via alternating direction method
    • Chen, C. H., He, B. S., Yuan, X. M.: Matrix completion via alternating direction method. IMA J. Numer. Anal. 32, 227-245 (2012).
    • (2012) IMA J. Numer. Anal. , vol.32 , pp. 227-245
    • Chen, C.H.1    He, B.S.2    Yuan, X.M.3
  • 12
    • 79952421740 scopus 로고    scopus 로고
    • Solving large-scale least squares covariance matrix problems by alternating direction methods
    • He, B. S., Xu, M. H., Yuan, X. M.: Solving large-scale least squares covariance matrix problems by alternating direction methods. SIAM J. Matrix Anal. Appl. 32, 136-152 (2011).
    • (2011) SIAM J. Matrix Anal. Appl. , vol.32 , pp. 136-152
    • He, B.S.1    Xu, M.H.2    Yuan, X.M.3
  • 13
    • 78149331304 scopus 로고    scopus 로고
    • Solving constrained total-variation problems via alternating direction methods
    • Ng, M. K., Weiss, P. A., Yuan, X. M.: Solving constrained total-variation problems via alternating direction methods. SIAM J. Sci. Comput. 32, 2710-2736 (2010).
    • (2010) SIAM J. Sci. Comput. , vol.32 , pp. 2710-2736
    • Ng, M.K.1    Weiss, P.A.2    Yuan, X.M.3
  • 14
    • 77957723364 scopus 로고    scopus 로고
    • A modified alternating direction method for convex quadratically constrained quadratic semidefinite programs
    • Sun, J., Zhang, S.: A modified alternating direction method for convex quadratically constrained quadratic semidefinite programs. Eur. J. Oper. Res. 207, 1210-1220 (2010).
    • (2010) Eur. J. Oper. Res. , vol.207 , pp. 1210-1220
    • Sun, J.1    Zhang, S.2
  • 15
    • 79957510064 scopus 로고    scopus 로고
    • Recovering low-rank and sparse components of matrices from incomplete and noisy observations
    • Tao, M., Yuan, X. M.: Recovering low-rank and sparse components of matrices from incomplete and noisy observations. SIAM J. Optim. 21, 57-81 (2011).
    • (2011) SIAM J. Optim. , vol.21 , pp. 57-81
    • Tao, M.1    Yuan, X.M.2
  • 17
    • 84881306037 scopus 로고    scopus 로고
    • Sparse and low-rank matrix decomposition via alternating direction method
    • (to appear)
    • Yuan, X. M., Yang, J. F.: Sparse and low-rank matrix decomposition via alternating direction method. Pac. J. Optim. (to appear).
    • Pac. J. Optim.
    • Yuan, X.M.1    Yang, J.F.2
  • 18
    • 80051762104 scopus 로고    scopus 로고
    • Distributed optimization and statistical learning via the alternating direction method of multipliers
    • Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Faund. Trends Mach. Learn. 3, 1-122 (2010).
    • (2010) Faund. Trends Mach. Learn. , vol.3 , pp. 1-122
    • Boyd, S.1    Parikh, N.2    Chu, E.3    Peleato, B.4    Eckstein, J.5
  • 19
    • 80051864161 scopus 로고    scopus 로고
    • Structured linear algebra problems in adaptive optics imaging
    • Bardsley, J. M., Knepper, S., Nagy, J.: Structured linear algebra problems in adaptive optics imaging. Adv. Comput. Math. 5(2-4), 103-117 (2011).
    • (2011) Adv. Comput. Math. , vol.5 , Issue.2-4 , pp. 103-117
    • Bardsley, J.M.1    Knepper, S.2    Nagy, J.3
  • 20
    • 0033438023 scopus 로고    scopus 로고
    • Proximal decomposition via alternating linearization
    • Kiwiel, K. C., Rosa, C. H., Ruszczyński, A.: Proximal decomposition via alternating linearization. SIAM J. Optim. 9, 668-689 (1999).
    • (1999) SIAM J. Optim. , vol.9 , pp. 668-689
    • Kiwiel, K.C.1    Rosa, C.H.2    Ruszczyński, A.3
  • 23
    • 84865692854 scopus 로고    scopus 로고
    • Alternating direction method with Gaussian back substitution for separable convex programming
    • (to appear)
    • He, B. S., Tao, M., Yuan, X. M.: Alternating direction method with Gaussian back substitution for separable convex programming. SIAM J. Optim. (to appear).
    • SIAM J. Optim.
    • He, B.S.1    Tao, M.2    Yuan, X.M.3
  • 25
    • 0004267646 scopus 로고
    • Princeton: Princeton University Press
    • Rockafellar, R. T.: Convex Analysis. Princeton University Press, Princeton (1970).
    • (1970) Convex Analysis
    • Rockafellar, R.T.1


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