메뉴 건너뛰기




Volumn 66, Issue 6, 2007, Pages 1428-1441

Convergence of the Polak-Ribiére-Polyak conjugate gradient method

Author keywords

Global convergence; PRP conjugate gradient method; Unconstrained optimization

Indexed keywords

FUNCTION EVALUATION; NUMERICAL ANALYSIS; OPTIMIZATION; PROBLEM SOLVING;

EID: 33845893334     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2006.02.001     Document Type: Article
Times cited : (28)

References (28)
  • 1
    • 84966275544 scopus 로고
    • Minimization of functions having Lipschits continuous partial derivatives
    • Armijo L. Minimization of functions having Lipschits continuous partial derivatives. Pacific J. Math. 16 (1966) 1-3
    • (1966) Pacific J. Math. , vol.16 , pp. 1-3
    • Armijo, L.1
  • 2
    • 0141467950 scopus 로고    scopus 로고
    • A spectral conjugate gradient method for unconstrained optimization
    • Birgin E.G., and Martinez J.M. A spectral conjugate gradient method for unconstrained optimization. Appl. Math. Optim. 43 (2001) 117-128
    • (2001) Appl. Math. Optim. , vol.43 , pp. 117-128
    • Birgin, E.G.1    Martinez, J.M.2
  • 3
    • 0141937371 scopus 로고
    • Rate of convergence of several conjugate gradient algorithms
    • Cohen A. Rate of convergence of several conjugate gradient algorithms. SIAM J. Numer. Anal. 9 (1972) 248-259
    • (1972) SIAM J. Numer. Anal. , vol.9 , pp. 248-259
    • Cohen, A.1
  • 4
    • 0035614397 scopus 로고    scopus 로고
    • New properties of a nonlinear conjugate gradient method
    • Dai Y.H. New properties of a nonlinear conjugate gradient method. Numer. Math. 89 (2001) 83-98
    • (2001) Numer. Math. , vol.89 , pp. 83-98
    • Dai, Y.H.1
  • 5
    • 0033266804 scopus 로고    scopus 로고
    • A nonlinear conjugate gradient method with a strong global convergence property
    • Dai Y.H., and Yuan Y. A nonlinear conjugate gradient method with a strong global convergence property. SIAM J. Optim. 10 1 (1999) 177-182
    • (1999) SIAM J. Optim. , vol.10 , Issue.1 , pp. 177-182
    • Dai, Y.H.1    Yuan, Y.2
  • 6
    • 33645875179 scopus 로고    scopus 로고
    • Testing different conjugate gradient methods for large-scale unconstrained optimization
    • Dai Y.H., and Ni Q. Testing different conjugate gradient methods for large-scale unconstrained optimization. J. Comput. Math. 21 3 (2003) 311-320
    • (2003) J. Comput. Math. , vol.21 , Issue.3 , pp. 311-320
    • Dai, Y.H.1    Ni, Q.2
  • 7
    • 21644488546 scopus 로고    scopus 로고
    • On the asymptotic behaviour of some new gradient methods
    • Dai Y.H., and Fletcher R. On the asymptotic behaviour of some new gradient methods. Math. Prog. 103 (2005) 541-559
    • (2005) Math. Prog. , vol.103 , pp. 541-559
    • Dai, Y.H.1    Fletcher, R.2
  • 8
    • 0000615669 scopus 로고
    • Function minimization by conjugate gradients
    • Fletcher R., and Reeves C. Function minimization by conjugate gradients. Comput. J. 7 (1964) 149-154
    • (1964) Comput. J. , vol.7 , pp. 149-154
    • Fletcher, R.1    Reeves, C.2
  • 9
    • 12344285803 scopus 로고    scopus 로고
    • Convergence conditions, line search algorithms and trust region implementations for the Polak Ribiére conjugate gradient method
    • Grippo L., and Lucidi S. Convergence conditions, line search algorithms and trust region implementations for the Polak Ribiére conjugate gradient method. Optim. Methods Softw. 20 1 (2005) 71-98
    • (2005) Optim. Methods Softw. , vol.20 , Issue.1 , pp. 71-98
    • Grippo, L.1    Lucidi, S.2
  • 10
    • 0013387067 scopus 로고    scopus 로고
    • A globally convergent version of the Polak-Ribiére conjugate gradient method
    • Grippo L., and Lucidi S. A globally convergent version of the Polak-Ribiére conjugate gradient method. Math. Prog. 78 (1997) 375-391
    • (1997) Math. Prog. , vol.78 , pp. 375-391
    • Grippo, L.1    Lucidi, S.2
  • 11
    • 0002824920 scopus 로고
    • Global convergence properties of conjugate gradient methods for optimization
    • Gilbert J.C., and Nocedal J. Global convergence properties of conjugate gradient methods for optimization. SIAM J. Optim. 2 1 (1992) 21-42
    • (1992) SIAM J. Optim. , vol.2 , Issue.1 , pp. 21-42
    • Gilbert, J.C.1    Nocedal, J.2
  • 12
    • 0003859310 scopus 로고
    • On steepest descent
    • Goldstein A.A. On steepest descent. SIAM J. Control 3 (1965) 147-151
    • (1965) SIAM J. Control , vol.3 , pp. 147-151
    • Goldstein, A.A.1
  • 13
    • 0000135303 scopus 로고
    • Method of conjugate gradient for solving linear systems
    • Hestenes M.R., and Stiefel E. Method of conjugate gradient for solving linear systems. J. Res. Nat. Bur. Stand. 49 (1952) 409-436
    • (1952) J. Res. Nat. Bur. Stand. , vol.49 , pp. 409-436
    • Hestenes, M.R.1    Stiefel, E.2
  • 17
    • 84972047841 scopus 로고
    • Theory of algorithm for unconstrained optimization
    • Nocedal J. Theory of algorithm for unconstrained optimization. Acta Numer. 1 (1992) 199-242
    • (1992) Acta Numer. , vol.1 , pp. 199-242
    • Nocedal, J.1
  • 19
    • 0001931644 scopus 로고
    • The conjugate gradient method in extreme problems
    • Polyak B.T. The conjugate gradient method in extreme problems. USSR Comput. Math. Math. Phys. 9 (1969) 94-112
    • (1969) USSR Comput. Math. Math. Phys. , vol.9 , pp. 94-112
    • Polyak, B.T.1
  • 20
    • 0035732192 scopus 로고    scopus 로고
    • Convergence of conjugate gradient methods without line search
    • Sun J., and Zhang J.P. Convergence of conjugate gradient methods without line search. Ann. Oper. Res. 103 (2001) 161-173
    • (2001) Ann. Oper. Res. , vol.103 , pp. 161-173
    • Sun, J.1    Zhang, J.P.2
  • 21
    • 10444285084 scopus 로고    scopus 로고
    • Quadratic cost flow and the conjugate gradient method
    • Sun J., Yang X.Q., and Chen X.D. Quadratic cost flow and the conjugate gradient method. European J. Oper. Res. 164 (2005) 104-114
    • (2005) European J. Oper. Res. , vol.164 , pp. 104-114
    • Sun, J.1    Yang, X.Q.2    Chen, X.D.3
  • 22
    • 0000618748 scopus 로고
    • Conjugate gradient methods with inexact line searches
    • Shanno D.F. Conjugate gradient methods with inexact line searches. Math. Oper. Res. 3 (1978) 244-256
    • (1978) Math. Oper. Res. , vol.3 , pp. 244-256
    • Shanno, D.F.1
  • 23
    • 0013495873 scopus 로고
    • On the convergence of a new conjugate gradient algorithm
    • Shanno D.F. On the convergence of a new conjugate gradient algorithm. SIAM J. Numer. Anal. 15 (1978) 1247-1257
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 1247-1257
    • Shanno, D.F.1
  • 24
    • 3042570018 scopus 로고    scopus 로고
    • Restricted PR conjugate gradient method and its global convergence
    • (in Chinese)
    • Shi Z.J. Restricted PR conjugate gradient method and its global convergence. Adv. Math. 31 1 (2002) 47-55 (in Chinese)
    • (2002) Adv. Math. , vol.31 , Issue.1 , pp. 47-55
    • Shi, Z.J.1
  • 25
    • 24944442546 scopus 로고    scopus 로고
    • Convergence of descent method without line search
    • Shi Z.J., and Shen J. Convergence of descent method without line search. Appl. Math. Comput. 167 (2005) 94-107
    • (2005) Appl. Math. Comput. , vol.167 , pp. 94-107
    • Shi, Z.J.1    Shen, J.2
  • 26
    • 34247548302 scopus 로고    scopus 로고
    • Step-size estimation for unconstrained optimization methods
    • Shi Z.J., and Shen J. Step-size estimation for unconstrained optimization methods. Comput. Appl. Math. 24 3 (2005) 1-18
    • (2005) Comput. Appl. Math. , vol.24 , Issue.3 , pp. 1-18
    • Shi, Z.J.1    Shen, J.2
  • 27
    • 0014492147 scopus 로고
    • Convergence conditions for ascent methods
    • Wolfe P. Convergence conditions for ascent methods. SIAM Rev. 11 (1969) 226-235
    • (1969) SIAM Rev. , vol.11 , pp. 226-235
    • Wolfe, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.