메뉴 건너뛰기




Volumn 6, Issue 1, 2014, Pages 77-102

Block splitting for distributed optimization

Author keywords

Alternating direction method of multipliers; Cone programming; Distributed optimization; Machine learning; Operator splitting; Proximal operators

Indexed keywords

ALTERNATING DIRECTION METHOD OF MULTIPLIERS; CONVEX OPTIMIZATION PROBLEMS; DISTRIBUTED COMPUTING ENVIRONMENT; DISTRIBUTED OPTIMIZATION; DOUGLAS-RACHFORD SPLITTING; NUMERICAL EXPERIMENTS; OPERATOR-SPLITTING; SPLITTING ALGORITHMS;

EID: 84898065835     PISSN: 18672949     EISSN: 18672957     Source Type: Journal    
DOI: 10.1007/s12532-013-0061-8     Document Type: Article
Times cited : (107)

References (32)
  • 1
    • 80051762104 scopus 로고    scopus 로고
    • Distributed optimization and statistical learning via the alternating direction method of multipliers
    • 10.1561/2200000016
    • Boyd, S.; Parikh, N.; Chu, E.; Peleato, B.; Eckstein, J.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 3(1), 1-122 (2011)
    • (2011) Found. Trends Mach. Learn. , vol.3 , Issue.1 , pp. 1-122
    • Boyd, S.1    Parikh, N.2    Chu, E.3    Peleato, B.4    Eckstein, J.5
  • 5
    • 0004055894 scopus 로고    scopus 로고
    • Cambridge University Press Cambridge 10.1017/CBO9780511804441 1058.90049
    • Boyd, S.; Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)
    • (2004) Convex Optimization
    • Boyd, S.1    Vandenberghe, L.2
  • 6
    • 79952297247 scopus 로고    scopus 로고
    • Alternating direction augmented Lagrangian methods for semidefinite programming
    • 10.1007/s12532-010-0017-1 1206.90088 2741485
    • Wen, Z.; Goldfarb, D.; Yin, W.: Alternating direction augmented Lagrangian methods for semidefinite programming. Math. Program. Comput. 2(3), 203-230 (2010)
    • (2010) Math. Program. Comput. , vol.2 , Issue.3 , pp. 203-230
    • Wen, Z.1    Goldfarb, D.2    Yin, W.3
  • 7
    • 85194972808 scopus 로고    scopus 로고
    • Regression shrinkage and selection via the lasso
    • 0850.62538 1379242
    • Tibshirani, R.: Regression shrinkage and selection via the lasso. J. R. Stat. Soc. Ser. B 58(1), 267-288 (1996)
    • (1996) J. R. Stat. Soc. Ser. B , vol.58 , Issue.1 , pp. 267-288
    • Tibshirani, R.1
  • 8
    • 0035889335 scopus 로고    scopus 로고
    • Intensity-modulated radiotherapy: Current status and issues of interest
    • Group, I.M.R.T.C.W.
    • Group, I.M.R.T.C.W.: Intensity-modulated radiotherapy: Current status and issues of interest. Int. J. Radiat. Oncol. Biol. Phys. 51(4), 880-914 (2001)
    • (2001) Int. J. Radiat. Oncol. Biol. Phys. , vol.51 , Issue.4 , pp. 880-914
  • 10
    • 0041356704 scopus 로고
    • Fonctions convexes duales et points proximaux dans un espace Hilbertien
    • 0118.10502 144188
    • Moreau, J.J.: Fonctions convexes duales et points proximaux dans un espace Hilbertien. Rep. Paris Acad. Sci. Ser. A 255, 2897-2899 (1962)
    • (1962) Rep. Paris Acad. Sci. Ser. A , vol.255 , pp. 2897-2899
    • Moreau, J.J.1
  • 11
    • 84884129062 scopus 로고    scopus 로고
    • Proximal algorithms
    • To appear
    • Parikh, N.; Boyd, S.: Proximal algorithms. Found. Trends Optim. 1(3), 1-108 (2013). To appear
    • (2013) Found. Trends Optim. , vol.1 , Issue.3 , pp. 1-108
    • Parikh, N.1    Boyd, S.2
  • 12
    • 0012231712 scopus 로고    scopus 로고
    • Operator-splitting methods for monotone affine variational inequalities, with a parallel application to optimal control
    • Eckstein, J.; Ferris, M.C.: Operator-splitting methods for monotone affine variational inequalities, with a parallel application to optimal control. INFORMS J. Comput. 10(2), 218-235 (1998) (Pubitemid 128669129)
    • (1998) INFORMS Journal on Computing , vol.10 , Issue.2 , pp. 218-235
    • Eckstein, J.1    Ferris, M.C.2
  • 13
    • 79952307213 scopus 로고    scopus 로고
    • Alternating direction algorithms for ℓ-1ℓ- 1 -problems in compressive sensing
    • 10.1137/090777761 1256.65060 2783194
    • Yang, J.; Zhang, Y.: Alternating direction algorithms for ℓ -1 ℓ -1 -problems in compressive sensing. SIAM J. Sci. Comput. 33(1), 250-278 (2011)
    • (2011) SIAM J. Sci. Comput. , vol.33 , Issue.1 , pp. 250-278
    • Yang, J.1    Zhang, Y.2
  • 15
    • 77953232934 scopus 로고    scopus 로고
    • Segmentation of ARX-models using sum-of-norms regularization
    • 10.1016/j.automatica.2010.03.013 1191.93139 2877195
    • Ohlsson, H.; Ljung, L.; Boyd, S.: Segmentation of ARX-models using sum-of-norms regularization. Automatica 46(6), 1107-1111 (2010)
    • (2010) Automatica , vol.46 , Issue.6 , pp. 1107-1111
    • Ohlsson, H.1    Ljung, L.2    Boyd, S.3
  • 18
    • 0033296299 scopus 로고    scopus 로고
    • Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones
    • 10.1080/10556789908805766 1778433
    • Sturm, J.: Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optim. Methods Softw. 11(1-4), 625-653 (1999)
    • (1999) Optim. Methods Softw. , vol.11 , Issue.1-4 , pp. 625-653
    • Sturm, J.1
  • 19
    • 0033295027 scopus 로고    scopus 로고
    • SDPT3: A MATLAB software package for semidefinite programming, version 1.3
    • 10.1080/10556789908805762 1778429
    • Toh, K.C.; Todd, M.J.; Tütüncü, R.H.: SDPT3: a MATLAB software package for semidefinite programming, version 1.3. Optim. Methods Softw. 11(1-4), 545-581 (1999)
    • (1999) Optim. Methods Softw. , vol.11 , Issue.1-4 , pp. 545-581
    • Toh, K.C.1    Todd, M.J.2    Tütüncü, R.H.3
  • 20
    • 84898073497 scopus 로고    scopus 로고
    • CVX Research, I.: CVX: Matlab software for disciplined convex programming, version 2.0 beta
    • CVX Research, I.: CVX: Matlab software for disciplined convex programming, version 2.0 beta. http://cvxr.com/cvx/examples (2012). Example library
    • (2012) Example Library
  • 22
    • 0002090173 scopus 로고
    • Symmetric quasi-definite matrices
    • 10.1137/0805005 0822.65017 1315706
    • Vanderbei, R.J.: Symmetric quasi-definite matrices. SIAM J. Optim. 5(1), 100-113 (1995)
    • (1995) SIAM J. Optim. , vol.5 , Issue.1 , pp. 100-113
    • Vanderbei, R.J.1
  • 23
    • 0039169750 scopus 로고    scopus 로고
    • Cholesky-based methods for sparse least squares: The benefits of regularization
    • Adams, L.; Nazareth, J.L. (eds.) SIAM, Philadelphia
    • Saunders, M.A.: Cholesky-based methods for sparse least squares: the benefits of regularization. In: Adams, L.; Nazareth, J.L. (eds.) Linear and Nonlinear Conjugate Gradient-Related Methods, pp. 92-100. SIAM, Philadelphia (1996)
    • (1996) Linear and Nonlinear Conjugate Gradient-Related Methods , pp. 92-100
    • Saunders, M.A.1
  • 24
    • 33745213090 scopus 로고    scopus 로고
    • Algorithm 8xx: A concise sparse Cholesky factorization package
    • 10.1145/1114268.1114277 1136.65311
    • Davis, T.A.: Algorithm 8xx: a concise sparse Cholesky factorization package. ACM Trans. Math. Softw. 31(4), 587-591 (2005)
    • (2005) ACM Trans. Math. Softw. , vol.31 , Issue.4 , pp. 587-591
    • Davis, T.A.1
  • 25
    • 0030491606 scopus 로고    scopus 로고
    • An approximate minimum degree ordering algorithm
    • 10.1137/S0895479894278952 0861.65021 1410707
    • Amestoy, P.; Davis, T.A.; Duff, I.S.: An approximate minimum degree ordering algorithm. SIAM J. Matrix Anal. Appl. 17(4), 886-905 (1996)
    • (1996) SIAM J. Matrix Anal. Appl. , vol.17 , Issue.4 , pp. 886-905
    • Amestoy, P.1    Davis, T.A.2    Duff, I.S.3
  • 26
    • 2942699190 scopus 로고    scopus 로고
    • Algorithm 837: AMD, an approximate minimum degree ordering algorithm
    • 10.1145/1024074.1024081 1070.65534 2124398
    • Amestoy, P.; Davis, T.A.; Duff, I.S.: Algorithm 837: AMD, an approximate minimum degree ordering algorithm. ACM Trans. Math. Softw. 30(3), 381-388 (2004)
    • (2004) ACM Trans. Math. Softw. , vol.30 , Issue.3 , pp. 381-388
    • Amestoy, P.1    Davis, T.A.2    Duff, I.S.3
  • 28
    • 0004675411 scopus 로고    scopus 로고
    • A sparse approximate inverse preconditioner for the conjugate gradient method
    • Benzi, M.; Meyer, C.D.; Tuma, M.: A sparse approximate inverse preconditioner for the conjugate gradient method. SIAM J. Sci. Comput. 17(5), 1135-1149 (1996) (Pubitemid 126598127)
    • (1996) SIAM Journal of Scientific Computing , vol.17 , Issue.5 , pp. 1135-1149
    • Benzi, M.1    Meyer, C.D.2    Tuma, M.3
  • 29
    • 0036867930 scopus 로고    scopus 로고
    • Preconditioning techniques for large linear systems: A survey
    • DOI 10.1006/jcph.2002.7176
    • Benzi, M.: Preconditioning techniques for large linear systems: a survey. J. Comput. Phys. 182(2), 418-477 (2002) (Pubitemid 36010064)
    • (2002) Journal of Computational Physics , vol.182 , Issue.2 , pp. 418-477
    • Benzi, M.1
  • 32
    • 0001467517 scopus 로고
    • Iterative refinement in floating point
    • 10.1145/321386.321394 0161.35501
    • Moler, C.B.: Iterative refinement in floating point. J. ACM 14(2), 316-321 (1967)
    • (1967) J. ACM , vol.14 , Issue.2 , pp. 316-321
    • Moler, C.B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.