메뉴 건너뛰기




Volumn 2, Issue 2, 2014, Pages 123-141

On the Linear Convergence of the Approximate Proximal Splitting Method for Non-smooth Convex Optimization

Author keywords

Block coordinate descent method; Convergence rate analysis; Convex optimization; Local error bound; Proximal splitting method

Indexed keywords

CONVEX OPTIMIZATION; FUNCTIONS; REGRESSION ANALYSIS;

EID: 84903559962     PISSN: 2194668X     EISSN: 21946698     Source Type: Journal    
DOI: 10.1007/s40305-014-0047-x     Document Type: Article
Times cited : (9)

References (36)
  • 1
    • 84873371070 scopus 로고    scopus 로고
    • Fast global convergence of gradient methods for high-dimensional statistical recovery
    • Agarwal, A., Negahban, S., Wainwright, M.: Fast global convergence of gradient methods for high-dimensional statistical recovery. Ann. Stat. 40, 2452-2482 (2012).
    • (2012) Ann. Stat. , vol.40 , pp. 2452-2482
    • Agarwal, A.1    Negahban, S.2    Wainwright, M.3
  • 2
    • 46249088758 scopus 로고    scopus 로고
    • Consistency of the group lasso and multiple kernel learning
    • Bach, F.: Consistency of the group lasso and multiple kernel learning. J. Mach. Learn. Res. 9, 1179-1225 (2008).
    • (2008) J. Mach. Learn. Res. , vol.9 , pp. 1179-1225
    • Bach, F.1
  • 4
    • 30844438177 scopus 로고    scopus 로고
    • Signal recovery by proximal forward-backward splitting
    • Combettes, P. L., Wajs, V. R.: Signal recovery by proximal forward-backward splitting. Multiscale Model. Simul. 4, 1168-1200 (2005).
    • (2005) Multiscale Model. Simul. , vol.4 , pp. 1168-1200
    • Combettes, P.L.1    Wajs, V.R.2
  • 5
    • 0009970312 scopus 로고
    • Local convergence analysis for successive inexact quadratic programming methods, Working Paper
    • School of Organization and Management, Yale University, New Haven
    • Dembo, R. S., Tulowizki, U.: Local convergence analysis for successive inexact quadratic programming methods, Working Paper. School of Organization and Management, Yale University, New Haven, (1984).
    • (1984)
    • Dembo, R.S.1    Tulowizki, U.2
  • 8
    • 0000005602 scopus 로고
    • The extra-gradient method for finding saddle points and other problems
    • Translated to English as Matecon
    • Korpelevich, G. M.: The extra-gradient method for finding saddle points and other problems. Ekon. i Mat Metody 12, 747-756 (1976). Translated to English as Matecon.
    • (1976) Ekon. I Mat Metody , vol.12 , pp. 747-756
    • Korpelevich, G.M.1
  • 9
    • 0000530015 scopus 로고
    • Remarks on the convergence of the matrix splitting algorithm for the symmetric linear complementarity problem
    • Li, W.: Remarks on the convergence of the matrix splitting algorithm for the symmetric linear complementarity problem. SIAM J. Optim. 3, 155-163 (1993).
    • (1993) SIAM J. Optim. , vol.3 , pp. 155-163
    • Li, W.1
  • 11
    • 0003095772 scopus 로고
    • Error bound and convergence analysis of matrix splitting algorithm for the affine variational inequality problem
    • Luo, Z.-Q., Tseng, P.: Error bound and convergence analysis of matrix splitting algorithm for the affine variational inequality problem. SIAM J. Optim. 2, 43-54 (1992).
    • (1992) SIAM J. Optim. , vol.2 , pp. 43-54
    • Luo, Z.-Q.1    Tseng, P.2
  • 12
    • 0026839499 scopus 로고
    • On the linear convergence of descent methods for convex essentially smooth minimization
    • Luo, Z.-Q., Tseng, P.: On the linear convergence of descent methods for convex essentially smooth minimization. SIAM J. Control Optim. 3, 408-425 (1992).
    • (1992) SIAM J. Control Optim. , vol.3 , pp. 408-425
    • Luo, Z.-Q.1    Tseng, P.2
  • 13
    • 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
  • 14
    • 84973041797 scopus 로고
    • Analysis of an approximate gradient projection method with applications to the back-propagation algorithm
    • Luo, Z.-Q., Tseng, P.: Analysis of an approximate gradient projection method with applications to the back-propagation algorithm. Optim. Methods Softw. 4, 85-101 (1994).
    • (1994) Optim. Methods Softw. , vol.4 , pp. 85-101
    • Luo, Z.-Q.1    Tseng, P.2
  • 15
    • 33947425580 scopus 로고    scopus 로고
    • Supervised group lasso with applications to microarray data analysis
    • Ma, S., Song, X., Huang, J.: Supervised group lasso with applications to microarray data analysis. BMC Bioinform. 8, 60 (2007).
    • (2007) BMC Bioinform. , vol.8 , pp. 60
    • Ma, S.1    Song, X.2    Huang, J.3
  • 17
    • 84964345548 scopus 로고
    • Convergence of iterates of an inexact matrix splitting algorithm for the symmetric monotone linear complementarity problem
    • Mangasarian, O. L.: Convergence of iterates of an inexact matrix splitting algorithm for the symmetric monotone linear complementarity problem. SIAM J. Optim. 1, 114-122 (1991).
    • (1991) SIAM J. Optim. , vol.1 , pp. 114-122
    • Mangasarian, O.L.1
  • 20
    • 0020143523 scopus 로고
    • On the convergence of the basic iterative method for the implicit complementarity problem
    • Pang, J.-S.: On the convergence of the basic iterative method for the implicit complementarity problem. J. Optim. Theory Appl. 37, 149-162 (1982).
    • (1982) J. Optim. Theory Appl. , vol.37 , pp. 149-162
    • Pang, J.-S.1
  • 21
    • 0022792007 scopus 로고
    • Inexact newton methods for nonlinear complementarity problem
    • Pang, J.-S.: Inexact newton methods for nonlinear complementarity problem. Math. Prog. 36(1), 54-71 (1986).
    • (1986) Math. Prog. , vol.36 , Issue.1 , pp. 54-71
    • Pang, J.-S.1
  • 22
    • 0001170028 scopus 로고
    • A posteriori error bounds for the linearly-constrained variational inequality problem
    • Pang, J.-S.: A posteriori error bounds for the linearly-constrained variational inequality problem. Math. Oper. Res. 12(3), 474-484 (1987).
    • (1987) Math. Oper. Res. , vol.12 , Issue.3 , pp. 474-484
    • Pang, J.-S.1
  • 23
    • 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, 1126-1153 (2013).
    • (2013) SIAM J. Optim. , vol.23 , pp. 1126-1153
    • Razaviyayn, M.1    Hong, M.2    Luo, Z.-Q.3
  • 24
    • 0004267646 scopus 로고
    • Princeton: Princeton University Press
    • Rockafellar, R. T.: Convex Analysis. Princeton University Press, Princeton (1970).
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 25
    • 0000788854 scopus 로고
    • The gradient projection method for non-linear programming, part I linear constraints
    • Rosen, J. B.: The gradient projection method for non-linear programming, part I linear constraints. J. Soc. Ind. Appl. Math. 8, 181-217 (1960).
    • (1960) J. Soc. Ind. Appl. Math. , vol.8 , pp. 181-217
    • Rosen, J.B.1
  • 26
    • 0001743783 scopus 로고
    • The gradient projection method for non-linear programming, part II non-linear constraints
    • Rosen, J. B.: The gradient projection method for non-linear programming, part II non-linear constraints. J. Soc. Ind. Appl. Math. 9, 514-532 (1961).
    • (1961) J. Soc. Ind. Appl. Math. , vol.9 , pp. 514-532
    • Rosen, J.B.1
  • 29
    • 0001287271 scopus 로고    scopus 로고
    • Regression shrinkage and selection via lasso
    • Tibshirani, R.: Regression shrinkage and selection via lasso. J. R. Stat. Soc. B 58, 267-288 (1996).
    • (1996) J. R. Stat. Soc. B , vol.58 , pp. 267-288
    • Tibshirani, R.1
  • 30
    • 0035533631 scopus 로고    scopus 로고
    • Convergence of block coordinate method for non-differentiable minimization
    • Tseng, P.: Convergence of block coordinate method for non-differentiable minimization. J. Optim. Theory Apppl. 109, 475-494 (2001).
    • (2001) J. Optim. Theory Apppl. , vol.109 , pp. 475-494
    • Tseng, P.1
  • 31
    • 77958113563 scopus 로고    scopus 로고
    • Approximation accuracy, gradient methods, and error bound for structured convex optimization
    • Tseng, P.: Approximation accuracy, gradient methods, and error bound for structured convex optimization. Math. Program. 125(2), 263-295 (2009).
    • (2009) Math. Program. , vol.125 , Issue.2 , pp. 263-295
    • Tseng, P.1
  • 32
    • 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. 117, 387-423 (2009).
    • (2009) Math. Program. , vol.117 , pp. 387-423
    • Tseng, P.1    Yun, S.2
  • 34
    • 84880719563 scopus 로고    scopus 로고
    • A proximal point algorithm for log-determinant optimization with group lasso regularization
    • Yang, J., Sun, D., Toh, K.-C.: A proximal point algorithm for log-determinant optimization with group lasso regularization. SIAM J. Optim. 23, 857-893 (2013).
    • (2013) SIAM J. Optim. , vol.23 , pp. 857-893
    • Yang, J.1    Sun, D.2    Toh, K.-C.3
  • 35
    • 33645035051 scopus 로고    scopus 로고
    • Model selection and estimation in regression with grouped variables
    • Yuan, M., Lin, Y.: Model selection and estimation in regression with grouped variables. J. R. Stat. Soc. B 68, 49-67 (2006).
    • (2006) J. R. Stat. Soc. B , vol.68 , pp. 49-67
    • Yuan, M.1    Lin, Y.2
  • 36
    • 84898953952 scopus 로고    scopus 로고
    • On the linear convergence of proximal splitting method for a class of nonsmooth convex minimization problems
    • Zhang, H., Jiang, J., Luo, Z.-Q.: On the linear convergence of proximal splitting method for a class of nonsmooth convex minimization problems. J. Oper. Res. Soc. China 1, 163-186 (2013).
    • (2013) J. Oper. Res. Soc. China , vol.1 , pp. 163-186
    • Zhang, H.1    Jiang, J.2    Luo, Z.-Q.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.