메뉴 건너뛰기




Volumn 233, Issue 2, 2009, Pages 519-530

A conjugate gradient method with descent direction for unconstrained optimization

Author keywords

Conjugate gradient method; Global convergence; Line search; Search direction; Unconstrained optimization

Indexed keywords

CONVERGENT RATE; GLOBAL CONVERGENCE; LINE SEARCH; LINE SEARCH TECHNIQUE; LINE SEARCHES; NUMERICAL RESULTS; SEARCH DIRECTION; STEEPEST DESCENT; TRUST REGION; UNCONSTRAINED OPTIMIZATION; UNCONSTRAINED OPTIMIZATION PROBLEMS;

EID: 69249208617     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2009.08.001     Document Type: Article
Times cited : (74)

References (36)
  • 1
    • 9944240601 scopus 로고    scopus 로고
    • A nonmonotone conjugate gradient algorithm for unconstrained optimization
    • Dai Y. A nonmonotone conjugate gradient algorithm for unconstrained optimization. J. Syst. Sci. Complex. 15 (2002) 139-145
    • (2002) J. Syst. Sci. Complex. , vol.15 , pp. 139-145
    • Dai, Y.1
  • 2
    • 33748075770 scopus 로고    scopus 로고
    • New nonlinear conjugate gradient formulas for large-scale unconstrained optimization problems
    • Wei Z., Li G., and Qi L. New nonlinear conjugate gradient formulas for large-scale unconstrained optimization problems. Appl. Math. Comput. 179 (2006) 407-430
    • (2006) Appl. Math. Comput. , vol.179 , pp. 407-430
    • Wei, Z.1    Li, G.2    Qi, L.3
  • 3
    • 33845762927 scopus 로고    scopus 로고
    • The convergence properties of some new conjugate gradient methods
    • Wei Z., Yao S., and Liu L. The convergence properties of some new conjugate gradient methods. Appl. Math. Comput. 183 (2006) 1341-1350
    • (2006) Appl. Math. Comput. , vol.183 , pp. 1341-1350
    • Wei, Z.1    Yao, S.2    Liu, L.3
  • 4
    • 40249107806 scopus 로고    scopus 로고
    • A new line search method with trust region for unconstrained optimization
    • Yuan G.L., and Lu X.W. A new line search method with trust region for unconstrained optimization. Commun. Appl. Nonlinear Anal. 1 15 (2008) 35-49
    • (2008) Commun. Appl. Nonlinear Anal. , vol.1 , Issue.15 , pp. 35-49
    • Yuan, G.L.1    Lu, X.W.2
  • 5
    • 67349205696 scopus 로고    scopus 로고
    • New two-point stepsize gradient methods for solving unconstrained optimization problems
    • Yuan G.L., Lu X.W., and Wei Z.X. New two-point stepsize gradient methods for solving unconstrained optimization problems. Natur. Sci. J. Xiangton Univ. 1 29 (2007) 13-15
    • (2007) Natur. Sci. J. Xiangton Univ. , vol.1 , Issue.29 , pp. 13-15
    • Yuan, G.L.1    Lu, X.W.2    Wei, Z.X.3
  • 6
    • 57749094411 scopus 로고    scopus 로고
    • New line search methods for unconstrained optimization
    • Yuan G.L., and Wei Z.X. New line search methods for unconstrained optimization. J. Korean Statist. Soc. 38 (2009) 29-39
    • (2009) J. Korean Statist. Soc. , vol.38 , pp. 29-39
    • Yuan, G.L.1    Wei, Z.X.2
  • 7
    • 40449112915 scopus 로고    scopus 로고
    • The superlinear convergence analysis of a nonmonotone BFGS algorithm on convex objective functions
    • Yuan G.L., and Wei Z.X. The superlinear convergence analysis of a nonmonotone BFGS algorithm on convex objective functions. Acta Math. Sin. (Engl. Ser.) 1 24 (2008) 35-42
    • (2008) Acta Math. Sin. (Engl. Ser.) , vol.1 , Issue.24 , pp. 35-42
    • Yuan, G.L.1    Wei, Z.X.2
  • 8
    • 77956768212 scopus 로고    scopus 로고
    • G.L. Yuan, Z.X. Wei, Convergence analysis of a modified BFGS method on convex minimizations, Comput. Optim. Appl., doi:10.1007/s10589-008-9219-0
    • G.L. Yuan, Z.X. Wei, Convergence analysis of a modified BFGS method on convex minimizations, Comput. Optim. Appl., doi:10.1007/s10589-008-9219-0
  • 9
    • 69249237868 scopus 로고    scopus 로고
    • A rank-one fitting method for unconstrained optimization problems
    • Yuan G.L., and Wei Z.X. A rank-one fitting method for unconstrained optimization problems. Math. Appl. 1 22 (2009) 118-122
    • (2009) Math. Appl. , vol.1 , Issue.22 , pp. 118-122
    • Yuan, G.L.1    Wei, Z.X.2
  • 10
    • 0033266804 scopus 로고    scopus 로고
    • A nonlinear conjugate gradient with a strong global convergence properties
    • Dai Y., and Yuan Y. A nonlinear conjugate gradient with a strong global convergence properties. SIAM J. Optim. 10 (2000) 177-182
    • (2000) SIAM J. Optim. , vol.10 , pp. 177-182
    • Dai, Y.1    Yuan, Y.2
  • 12
    • 0000615669 scopus 로고
    • Function minimization bu conjugate gradients
    • Fletcher R., and Reeves C. Function minimization bu conjugate gradients. Compute. J. 7 (1964) 149-154
    • (1964) Compute. J. , vol.7 , pp. 149-154
    • Fletcher, R.1    Reeves, C.2
  • 13
    • 0000135303 scopus 로고
    • Method of conjugate gradient for solving linear equations
    • Hestenes M.R., and Stiefel E. Method of conjugate gradient for solving linear equations. 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
  • 14
    • 0026142704 scopus 로고
    • Effcient generalized conjugate gradient algorithms, part 1: Theory
    • Liu Y., and Storey C. Effcient generalized conjugate gradient algorithms, part 1: Theory. J. Optim. Theory Appl. 69 (1992) 17-41
    • (1992) J. Optim. Theory Appl. , vol.69 , pp. 17-41
    • Liu, Y.1    Storey, C.2
  • 18
    • 0001219541 scopus 로고
    • Nonconvex minimization calculations and the conjugate gradient method
    • Spinger-Verlag, Berlin
    • Powell M.J.D. Nonconvex minimization calculations and the conjugate gradient method. Lecture Notes in Mathematics vol. 1066 (1984), Spinger-Verlag, Berlin 122-141
    • (1984) Lecture Notes in Mathematics , vol.1066 , pp. 122-141
    • Powell, M.J.D.1
  • 19
    • 0002824920 scopus 로고
    • Global convergence properties of conugate gradient methods for optimization
    • Gibert J.C., and Nocedal J. Global convergence properties of conugate gradient methods for optimization. SIAM J. Optimiz. 2 (1992) 21-42
    • (1992) SIAM J. Optimiz. , vol.2 , pp. 21-42
    • Gibert, J.C.1    Nocedal, J.2
  • 20
    • 0035730017 scopus 로고    scopus 로고
    • An efficient hybrid conjugate gradient method for unconstrained optimization
    • Dai Y., and Yuan Y. An efficient hybrid conjugate gradient method for unconstrained optimization. Ann. Oper. Res. 103 (2001) 33-47
    • (2001) Ann. Oper. Res. , vol.103 , pp. 33-47
    • Dai, Y.1    Yuan, Y.2
  • 21
    • 0025387662 scopus 로고
    • Efficient hybrid conjugate gradient techniques
    • Ahmed T., and Storey D. Efficient hybrid conjugate gradient techniques. J. Optim. Theory Appl. 64 (1990) 379-394
    • (1990) J. Optim. Theory Appl. , vol.64 , pp. 379-394
    • Ahmed, T.1    Storey, D.2
  • 22
    • 77957214026 scopus 로고
    • Descent property and global convergence of the Flecher-Reeves method with inexact line search
    • Al-Baali A. Descent property and global convergence of the Flecher-Reeves method with inexact line search. IMA J. Numer. Anal. 5 (1985) 121-124
    • (1985) IMA J. Numer. Anal. , vol.5 , pp. 121-124
    • Al-Baali, A.1
  • 23
    • 0026253861 scopus 로고
    • Global convergence result for conjugate method
    • Hu Y.F., and Storey C. Global convergence result for conjugate method. J. Optim. Theory Appl. 71 (1991) 399-405
    • (1991) J. Optim. Theory Appl. , vol.71 , pp. 399-405
    • Hu, Y.F.1    Storey, C.2
  • 24
    • 0013387067 scopus 로고    scopus 로고
    • A globally convergent version of the Polak-Ribière gradient method
    • Grippo L., and Lucidi S. A globally convergent version of the Polak-Ribière gradient method. Math. Program. 78 (1997) 375-391
    • (1997) Math. Program. , vol.78 , pp. 375-391
    • Grippo, L.1    Lucidi, S.2
  • 25
    • 33144465578 scopus 로고    scopus 로고
    • A new conjugate gradient method with guaranteed descent and an efficient line search
    • Hager W.W., and Zhang H.C. A new conjugate gradient method with guaranteed descent and an efficient line search. SIAM J. Optim. 1 16 (2005) 170-192
    • (2005) SIAM J. Optim. , vol.1 , Issue.16 , pp. 170-192
    • Hager, W.W.1    Zhang, H.C.2
  • 27
    • 67650498880 scopus 로고    scopus 로고
    • Modified nonlinear conjugate gradient methods with sufficient descent property for large-scale optimization problems
    • Yuan G.L. Modified nonlinear conjugate gradient methods with sufficient descent property for large-scale optimization problems. Optim. Lett. 3 (2009) 11-21
    • (2009) Optim. Lett. , vol.3 , pp. 11-21
    • Yuan, G.L.1
  • 28
    • 58149527130 scopus 로고    scopus 로고
    • A modified PRP conjugate gradient method
    • Yuan G.L., and Lu X.W. A modified PRP conjugate gradient method. Ann. Oper. Res. 166 (2009) 73-90
    • (2009) Ann. Oper. Res. , vol.166 , pp. 73-90
    • Yuan, G.L.1    Lu, X.W.2
  • 29
    • 33749621811 scopus 로고    scopus 로고
    • A descent modified Polak-Ribière-Polyak conjugate method and its global convergence
    • Zhang L., Zhou W., and Li D. A descent modified Polak-Ribière-Polyak conjugate method and its global convergence. IMA J. Numer. Anal. 26 (2006) 629-649
    • (2006) IMA J. Numer. Anal. , vol.26 , pp. 629-649
    • Zhang, L.1    Zhou, W.2    Li, D.3
  • 30
    • 0001854432 scopus 로고
    • Nonlinear programming computational methods
    • Abadie J. (Ed), NorthHolllad, Amsterdam
    • Zoutendijk G. Nonlinear programming computational methods. In: Abadie J. (Ed). Integer and Nonlinear Programming (1970), NorthHolllad, Amsterdam 37-86
    • (1970) Integer and Nonlinear Programming , pp. 37-86
    • Zoutendijk, G.1
  • 34
    • 28244496090 scopus 로고    scopus 로고
    • Benchmarking optimization software with performance profiles
    • Dolan E.D., and Moré J.J. Benchmarking optimization software with performance profiles. Math. Program. 91 (2002) 201-213
    • (2002) Math. Program. , vol.91 , pp. 201-213
    • Dolan, E.D.1    Moré, J.J.2
  • 35
    • 4444343782 scopus 로고    scopus 로고
    • Convergence of line search methods for unconstrained optimization
    • Shi Z.J. Convergence of line search methods for unconstrained optimization. Appl. Math. Comput. 157 (2004) 393-405
    • (2004) Appl. Math. Comput. , vol.157 , pp. 393-405
    • Shi, Z.J.1
  • 36
    • 9944262108 scopus 로고    scopus 로고
    • A nonmonotone line search technique and its application to unconstrained optimization
    • Zhang H.C., and Hager W.W. A nonmonotone line search technique and its application to unconstrained optimization. SIAM J. Optim 4 14 (2004) 1043-1056
    • (2004) SIAM J. Optim , vol.4 , Issue.14 , pp. 1043-1056
    • Zhang, H.C.1    Hager, W.W.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.