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Volumn 151, Issue 1, 2015, Pages 3-34

Coordinate descent algorithms

Author keywords

Coordinate descent; Parallel numerical computing; Randomized algorithms

Indexed keywords

ARTIFICIAL INTELLIGENCE; LEARNING SYSTEMS; OPTIMIZATION; PROBLEM SOLVING;

EID: 84940008519     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-015-0892-3     Document Type: Article
Times cited : (1469)

References (56)
  • 1
    • 77953092582 scopus 로고    scopus 로고
    • Proximal alternating minimization and projection methods for nonconvex problems: an approach based on the Kurdyka-Lojasiewicz inequality
    • Attouch, H., Bolte, J., Redont, P., Soubeyran, A.: Proximal alternating minimization and projection methods for nonconvex problems: an approach based on the Kurdyka-Lojasiewicz inequality. Math. Oper. Res. 35(2), 438–457 (2010)
    • (2010) Math. Oper. Res. , vol.35 , Issue.2 , pp. 438-457
    • Attouch, H.1    Bolte, J.2    Redont, P.3    Soubeyran, A.4
  • 2
    • 85014561619 scopus 로고    scopus 로고
    • A fast iterative shrinkage-threshold algorithm for linear inverse problems
    • Beck, A., Teboulle, M.: A fast iterative shrinkage-threshold algorithm for linear inverse problems. SIAM J. Imaging Sci. 2(1), 183–202 (2009)
    • (2009) SIAM J. Imaging Sci. , vol.2 , Issue.1 , pp. 183-202
    • Beck, A.1    Teboulle, M.2
  • 3
    • 84892868336 scopus 로고    scopus 로고
    • On the convergence of block coordinate descent methods
    • Beck, A., Tetruashvili, L.: On the convergence of block coordinate descent methods. SIAM J. Optim. 23(4), 2037–2060 (2013)
    • (2013) SIAM J. Optim. , vol.23 , Issue.4 , pp. 2037-2060
    • Beck, A.1    Tetruashvili, L.2
  • 6
    • 84905580784 scopus 로고    scopus 로고
    • Proximal alternating linearized minimization for nonconvex and nonsmooth problems
    • Bolte, J., Sabach, S., Teboulle, M.: Proximal alternating linearized minimization for nonconvex and nonsmooth problems. Math. Program. Ser. A 146, 1–36 (2014)
    • (2014) Math. Program. Ser. A , vol.146
    • Bolte, J.1    Sabach, S.2    Teboulle, M.3
  • 7
    • 0030109399 scopus 로고    scopus 로고
    • A unified approach to statistical tomography using coordinate descent optimization
    • Bouman, C.A., Sauer, K.: A unified approach to statistical tomography using coordinate descent optimization. IEEE Trans. Image Process. 5(3), 480–492 (1996)
    • (1996) IEEE Trans. Image Process. , vol.5 , Issue.3 , pp. 480-492
    • Bouman, C.A.1    Sauer, K.2
  • 8
    • 80051762104 scopus 로고    scopus 로고
    • Distributed optimization and statistical learning via the alternating direction methods of multipliers
    • Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J.: Distributed optimization and statistical learning via the alternating direction methods of multipliers. Found. Trends Mach. Learn. 3(1), 1–122 (2011)
    • (2011) Found. Trends Mach. Learn. , vol.3 , Issue.1
    • Boyd, S.1    Parikh, N.2    Chu, E.3    Peleato, B.4    Eckstein, J.5
  • 10
    • 80053013888 scopus 로고    scopus 로고
    • Coordinate descent algroithms for nonconvex penalized regression, with applications to biological feature selection
    • Breheny, P., Huang, J.: Coordinate descent algroithms for nonconvex penalized regression, with applications to biological feature selection. Ann. Appl. Stat. 5(1), 232–252 (2011)
    • (2011) Ann. Appl. Stat. , vol.5 , Issue.1 , pp. 232-252
    • Breheny, P.1    Huang, J.2
  • 11
    • 0037406075 scopus 로고    scopus 로고
    • Cyclic coordinate descent: a robotics algorithm for protein loop closure
    • Canutescu, A.A., Dunbrack, R.L.: Cyclic coordinate descent: a robotics algorithm for protein loop closure. Protein Sci. 12(5), 963–972 (2003)
    • (2003) Protein Sci. , vol.12 , Issue.5 , pp. 963-972
    • Canutescu, A.A.1    Dunbrack, R.L.2
  • 12
    • 48849104146 scopus 로고    scopus 로고
    • Coordinate descent method for large-scale l2-loss linear support vector machines
    • Chang, K., Hsieh, C., Lin, C.: Coordinate descent method for large-scale l2-loss linear support vector machines. J. Mach. Learn. Res. 9, 1369–1398 (2008)
    • (2008) J. Mach. Learn. Res. , vol.9 , pp. 1369-1398
    • Chang, K.1    Hsieh, C.2    Lin, C.3
  • 13
    • 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
  • 15
    • 84939937630 scopus 로고    scopus 로고
    • Fercoq, O., Qu, Z., Richtarik, P., Takac, M.: Fast distributed coordinate descent for non-strongly convex losses (2014)
    • Fercoq, O., Qu, Z., Richtarik, P., Takac, M.: Fast distributed coordinate descent for non-strongly convex losses (2014). arxiv:1405.5300
  • 16
    • 84912542181 scopus 로고    scopus 로고
    • Accelerated, parallel, and proximal coordinate descent. Technical Report, School of Mathematics
    • Fercoq, O., Richtarik, P.: Accelerated, parallel, and proximal coordinate descent. Technical Report, School of Mathematics, University of Edinburgh (2013). arXiv:1312.5799
    • University of Edinburgh (2013). arXiv , pp. 5799
    • Fercoq, O.1    Richtarik, P.2
  • 17
    • 0001145272 scopus 로고
    • A coordinate descent method for the bilevel O-D matrix adjustment problem
    • Florian, M., Chen, Y.: A coordinate descent method for the bilevel O-D matrix adjustment problem. Int. Trans. Oper. Res. 2(2), 165–179 (1995)
    • (1995) Int. Trans. Oper. Res. , vol.2 , Issue.2 , pp. 165-179
    • Florian, M.1    Chen, Y.2
  • 18
    • 45849134070 scopus 로고    scopus 로고
    • Sparse inverse covariance estimation with the graphical lasso
    • Friedman, J., Hastie, T., Tibshirani, R.: Sparse inverse covariance estimation with the graphical lasso. Biostatistics 9(3), 432–441 (2008)
    • (2008) Biostatistics , vol.9 , Issue.3 , pp. 432-441
    • Friedman, J.1    Hastie, T.2    Tibshirani, R.3
  • 19
    • 77950537175 scopus 로고    scopus 로고
    • Regularization paths for generalized linear models via coordinate descent
    • Friedman, J.H., Hastie, T., Tibshirani, R.: Regularization paths for generalized linear models via coordinate descent. J. Stat. Softw. 33(1), 1–22 (2010)
    • (2010) J. Stat. Softw. , vol.33 , Issue.1
    • Friedman, J.H.1    Hastie, T.2    Tibshirani, R.3
  • 23
    • 84893479942 scopus 로고    scopus 로고
    • Efficient accelerated coordinate descent methods and faster algorihtms for solving linear systems
    • Lee, Y.T., Sidford, A.: Efficient accelerated coordinate descent methods and faster algorihtms for solving linear systems. In: 54th Annual Symposium on Foundations of Computer Science, pp. 147–156 (2013)
    • (2013) 54th Annual Symposium on Foundations of Computer Science , pp. 147-156
    • Lee, Y.T.1    Sidford, A.2
  • 24
    • 77956625417 scopus 로고    scopus 로고
    • Randomized methods for linear constraints: convergence rates and conditioning
    • Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Math. Oper. Res. 35(3), 641–654 (2010)
    • (2010) Math. Oper. Res. , vol.35 , Issue.3 , pp. 641-654
    • Leventhal, D.1    Lewis, A.S.2
  • 25
    • 84973248304 scopus 로고    scopus 로고
    • An accelerated proximal coordinate gradient method and its application to empirical risk minimization. Technical Report
    • Lin, Q., Lu, Z., Xiao, L.: An accelerated proximal coordinate gradient method and its application to empirical risk minimization. Technical Report, Microsoft Research (2014). arXiv:1407.1296
    • Microsoft Research (2014). arXiv , pp. 1407
    • Lin, Q.1    Lu, Z.2    Xiao, L.3
  • 26
    • 71149111015 scopus 로고    scopus 로고
    • Lockwise coordinate descent procedures for the multi-task lasso, with applications to neural semantic basis discovery
    • ACM, New York, NY, USA
    • Liu, H., Palatucci, M., Zhang, J.: Lockwise coordinate descent procedures for the multi-task lasso, with applications to neural semantic basis discovery. In: Proceedings of the 26th Annual International Conference on Machine Learning. ICML ’09, pp. 649–656. ACM, New York, NY, USA (2009)
    • (2009) Proceedings of the 26th Annual International Conference on Machine Learning. ICML ’09 , pp. 649-656
    • Liu, H.1    Palatucci, M.2    Zhang, J.3
  • 27
    • 84973234482 scopus 로고    scopus 로고
    • Asynchronous stochastic coordinate descent: parallelism and convergence properties. Technical Report, University of Wisconsin
    • Liu, J., Wright, S.J.: Asynchronous stochastic coordinate descent: parallelism and convergence properties. Technical Report, University of Wisconsin, Madison. (2014). (To appear in SIAM Journal on Optimization). arXiv:1403.3862
    • Madison. (2014). (To appear in SIAM Journal on Optimization). arXiv , pp. 3862
    • Liu, J.1    Wright, S.J.2
  • 28
    • 84973231219 scopus 로고
    • An asynchronous parallel stochastic coordinate descent algorithm. Technical Report, Computer Sciences Department, University of Wisconsin-Madison (2013)
    • Liu, J., Wright, S.J., Ré, C., Bittorf, V., Sridhar, S.: An asynchronous parallel stochastic coordinate descent algorithm. Technical Report, Computer Sciences Department, University of Wisconsin-Madison (2013). (To appear in Journal of Machine Learning Research). arXiv:1311.1873
    • (1873) (To appear in Journal of Machine Learning Research). arXiv , pp. 1311
    • Liu, J.1    Wright, S.J.2    Ré, C.3    Bittorf, V.4    Sridhar, S.5
  • 29
    • 84973228539 scopus 로고    scopus 로고
    • An accelerated randomized Kaczmarz algorithm. Technical Report, Computer Sciences Department, University of Wisconsin-Madison (2013)
    • Liu, J., Wright, S.J., Sridhar, S.: An accelerated randomized Kaczmarz algorithm. Technical Report, Computer Sciences Department, University of Wisconsin-Madison (2013). (To appear in Mathematics of Computation). arXiv 1310.2887
    • (To appear in Mathematics of Computation). arXiv , pp. 1310
    • Liu, J.1    Wright, S.J.2    Sridhar, S.3
  • 30
    • 0026678659 scopus 로고
    • On the convergence of the coordinate descent method for convex differentiable minimization
    • Luo, Z.Q., Tseng, P.: On the convergence of the coordinate descent method for convex differentiable minimization. J. Optim. Theory Appl. 72(1), 7–35 (1992)
    • (1992) J. Optim. Theory Appl. , vol.72 , Issue.1 , pp. 7-35
    • Luo, Z.Q.1    Tseng, P.2
  • 31
    • 21344480786 scopus 로고
    • Error bounds and convergence analysis of feasible descent methods: a general approach
    • Luo, Z.Q., Tseng, P.: Error bounds and convergence analysis of feasible descent methods: a general approach. Ann. Oper. Res. 46, 157–178 (1993)
    • (1993) Ann. Oper. Res. , vol.46 , pp. 157-178
    • Luo, Z.Q.1    Tseng, P.2
  • 32
    • 84937848805 scopus 로고    scopus 로고
    • Distributed block coordinate descent for minimizing partially separable functions
    • Marecek, J., Richtarik, P., Takac, M.: Distributed block coordinate descent for minimizing partially separable functions. Technical Report arXiv:1406.0238 (2014)
    • (2014) Technical Report arXiv , vol.1406 , pp. 0238
    • Marecek, J.1    Richtarik, P.2    Takac, M.3
  • 33
    • 80052694528 scopus 로고    scopus 로고
    • SparseNet: coordinate descent with nonconvex penalties
    • Mazumder, R., Friedman, J.H., Hastie, T.: SparseNet: coordinate descent with nonconvex penalties. J. Am. Stat. Assoc. 106, 1125–1138 (2011)
    • (2011) J. Am. Stat. Assoc. , vol.106 , pp. 1125-1138
    • Mazumder, R.1    Friedman, J.H.2    Hastie, T.3
  • 34
    • 84973245648 scopus 로고    scopus 로고
    • Distributed random coordinate descent method for composite minimization. Technical Report 1–41
    • Necoara, I., Clipici, D.: Distributed random coordinate descent method for composite minimization. Technical Report 1–41, University Politehnica Bucharest (2013)
    • (2013) University Politehnica Bucharest
    • Necoara, I.1    Clipici, D.2
  • 35
    • 34548480020 scopus 로고
    • A method for unconstrained convex problem with the rate of convergence (Formula presented.)
    • Nesterov, Y.: A method for unconstrained convex problem with the rate of convergence $$O(1/k^2)$$O(1/k2). Doklady AN SSSR 269, 543–547 (1983)
    • (1983) Doklady AN SSSR , vol.269 , pp. 543-547
    • Nesterov, Y.1
  • 37
    • 84865692149 scopus 로고    scopus 로고
    • Efficiency of coordinate descent methods on huge-scale optimization problems
    • Nesterov, Y.: Efficiency of coordinate descent methods on huge-scale optimization problems. SIAM J. Optim. 22, 341–362 (2012)
    • (2012) SIAM J. Optim. , vol.22 , pp. 341-362
    • Nesterov, Y.1
  • 40
    • 84943588662 scopus 로고    scopus 로고
    • Efficient random coordinate descent algorithms for large-scale structured nonconvex optimization. J. Glob
    • Patrascu, A., Necoara, I.: Efficient random coordinate descent algorithms for large-scale structured nonconvex optimization. J. Glob. Optim. (2013). doi:10.1007/s10898-014-0151-9
    • (2013) Optim
    • Patrascu, A.1    Necoara, I.2
  • 41
    • 0003120218 scopus 로고    scopus 로고
    • Fast training of support vector machines using sequential minimal optimization
    • Schölkopf B, Burges CJC, Smola AJ, (eds), MIT Press, Cambridge
    • Platt, J.C.: Fast training of support vector machines using sequential minimal optimization. In: Schölkopf, B., Burges, C.J.C., Smola, A.J. (eds.) Advances in Kernel Methods—Support Vector Learning, pp. 185–208. MIT Press, Cambridge (1999)
    • (1999) Advances in Kernel Methods—Support Vector Learning , pp. 185-208
    • Platt, J.C.1
  • 43
    • 0001258795 scopus 로고
    • On search directions for minimization algorithms
    • Powell, M.J.D.: On search directions for minimization algorithms. Math. Program. 4, 193–201 (1973)
    • (1973) Math. Program. , vol.4 , pp. 193-201
    • Powell, M.J.D.1
  • 44
    • 84880570485 scopus 로고    scopus 로고
    • A unified convergence analysis of block successive minimization methods for nonsmooth optimization
    • Razaviyayn, M., Hong, M., Luo, Z.Q.: A unified convergence analysis of block successive minimization methods for nonsmooth optimization. SIAM J. Optim. 23(2), 1126–1153 (2013)
    • (2013) SIAM J. Optim. , vol.23 , Issue.2 , pp. 1126-1153
    • Razaviyayn, M.1    Hong, M.2    Luo, Z.Q.3
  • 45
    • 78549288866 scopus 로고    scopus 로고
    • Guaranteed minimum-rank solutions to linear matrix equations via nuclear norm minimization
    • Recht, B., Fazel, M., Parrilo, P.: Guaranteed minimum-rank solutions to linear matrix equations via nuclear norm minimization. SIAM Rev. 52(3), 471–501 (2010)
    • (2010) SIAM Rev. , vol.52 , Issue.3 , pp. 471-501
    • Recht, B.1    Fazel, M.2    Parrilo, P.3
  • 46
    • 84882256468 scopus 로고    scopus 로고
    • Parallel coordinate descent methods for big data optimization. Technical Report, School of Mathematics
    • Richtarik, P., Takac, M.: Parallel coordinate descent methods for big data optimization. Technical Report, School of Mathematics, University of Edinburgh (2013). arXiv:1212.0873
    • University of Edinburgh (2013). arXiv , pp. 0873
    • Richtarik, P.1    Takac, M.2
  • 47
    • 84897116612 scopus 로고    scopus 로고
    • Iteration complexity of a randomized block-coordinate descent methods for minimizing a composite function
    • Richtarik, P., Takac, M.: Iteration complexity of a randomized block-coordinate descent methods for minimizing a composite function. Math. Program. Ser. A 144(1), 1–38 (2014)
    • (2014) Math. Program. Ser. A , vol.144 , Issue.1
    • Richtarik, P.1    Takac, M.2
  • 48
    • 0004267646 scopus 로고
    • Princeton University Press, Princeton
    • Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 49
    • 23044521122 scopus 로고    scopus 로고
    • Block coordinate relaxation methods for nonparametric wavelet denoising
    • Sardy, S., Bruce, A., Tseng, P.: Block coordinate relaxation methods for nonparametric wavelet denoising. J. Comput. Graph. Stat. 9, 361–379 (2000)
    • (2000) J. Comput. Graph. Stat. , vol.9 , pp. 361-379
    • Sardy, S.1    Bruce, A.2    Tseng, P.3
  • 50
    • 79960131832 scopus 로고    scopus 로고
    • Stochastic methods for (Formula presented.)-regularized loss minimization
    • Shalev-Shwartz, S., Tewari, A.: Stochastic methods for $$\ell _1$$ℓ1-regularized loss minimization. J. Mach. Learn. Res. 12, 1865–1892 (2011)
    • (2011) J. Mach. Learn. Res. , vol.12 , pp. 1865-1892
    • Shalev-Shwartz, S.1    Tewari, A.2
  • 51
    • 84875134236 scopus 로고    scopus 로고
    • Stochastic dual coordinate ascent mehods for regularized loss minimization
    • Shalev-Shwartz, S., Zhang, T.: Stochastic dual coordinate ascent mehods for regularized loss minimization. J. Mach. Learn. Res. 14, 437–469 (2013)
    • (2013) J. Mach. Learn. Res. , vol.14 , pp. 437-469
    • Shalev-Shwartz, S.1    Zhang, T.2
  • 52
    • 67349206945 scopus 로고    scopus 로고
    • A randomized Kaczmarz algorithm with exponential convergence
    • Strohmer, T., Vershynin, R.: A randomized Kaczmarz algorithm with exponential convergence. J. Fourier Anal. Appl. 15, 262–278 (2009)
    • (2009) J. Fourier Anal. Appl. , vol.15 , pp. 262-278
    • Strohmer, T.1    Vershynin, R.2
  • 53
    • 85194972808 scopus 로고    scopus 로고
    • Regression shrinkage and selection via the LASSO
    • Tibshirani, R.: Regression shrinkage and selection via the LASSO. J. R. Stat. Soc. B 58, 267–288 (1996)
    • (1996) J. R. Stat. Soc. B , vol.58 , pp. 267-288
    • Tibshirani, R.1
  • 54
    • 0035533631 scopus 로고    scopus 로고
    • Convergence of a block coordinate descent method for nondifferentiable minimization
    • Tseng, P.: Convergence of a block coordinate descent method for nondifferentiable minimization. J. Optim. Theory Appl. 109(3), 475–494 (2001)
    • (2001) J. Optim. Theory Appl. , vol.109 , Issue.3 , pp. 475-494
    • Tseng, P.1
  • 55
    • 46749146509 scopus 로고    scopus 로고
    • A coordinate gradient descent method for nonsmooth separable minimization
    • Tseng, P., Yun, S.: A coordinate gradient descent method for nonsmooth separable minimization. Math. Program. Ser. B 117, 387–423 (2009)
    • (2009) Math. Program. Ser. B , vol.117 , pp. 387-423
    • Tseng, P.1    Yun, S.2
  • 56
    • 0000828127 scopus 로고    scopus 로고
    • Optical diffusion tomography by iterative-coordinate-descent optimization in a bayesian framework
    • Ye, J.C., Webb, K.J., Bouman, C.A., Millane, R.P.: Optical diffusion tomography by iterative-coordinate-descent optimization in a bayesian framework. J. Opt. Soc. Am. A 16(10), 2400–2412 (1999)
    • (1999) J. Opt. Soc. Am. A , vol.16 , Issue.10 , pp. 2400-2412
    • Ye, J.C.1    Webb, K.J.2    Bouman, C.A.3    Millane, R.P.4


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