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Volumn 159, Issue 1, 2013, Pages 159-182

Another Conjugate Gradient Algorithm with Guaranteed Descent and Conjugacy Conditions for Large-scale Unconstrained Optimization

Author keywords

Conjugacy condition; Conjugate gradient; Descent condition; Unconstrained optimization; Wolfe line search

Indexed keywords

FUNCTIONS; OPTIMIZATION;

EID: 84884514636     PISSN: 00223239     EISSN: 15732878     Source Type: Journal    
DOI: 10.1007/s10957-013-0285-9     Document Type: Article
Times cited : (25)

References (29)
  • 1
    • 0024631560 scopus 로고
    • Some history of the conjugate gradient and Lanczos algorithms: 1948-1976
    • Golub, G. H., O'Leary, D. P.: Some history of the conjugate gradient and Lanczos algorithms: 1948-1976. SIAM Rev. 31, 50-102 (1989).
    • (1989) SIAM Rev. , vol.31 , pp. 50-102
    • Golub, G.H.1    O'Leary, D.P.2
  • 2
    • 29444440836 scopus 로고    scopus 로고
    • Conjugate gradients and related KMP algorithms: the beginnings
    • L. Adams and J. L. Nazareth (Eds.), Philadelphia: SIAM
    • O'Leary, D. P.: Conjugate gradients and related KMP algorithms: the beginnings. In: Adams, L., Nazareth, J. L. (eds.) Linear and Nonlinear Conjugate Gradient-Related Methods, pp. 1-8. SIAM, Philadelphia (1996).
    • (1996) Linear and Nonlinear Conjugate Gradient-Related Methods , pp. 1-8
    • O'Leary, D.P.1
  • 3
    • 33745276908 scopus 로고    scopus 로고
    • A survey of nonlinear conjugate gradient methods
    • Hager, W. W., Zhang, H.: A survey of nonlinear conjugate gradient methods. Pac. J. Optim. 2, 35-58 (2006).
    • (2006) Pac. J. Optim. , vol.2 , pp. 35-58
    • Hager, W.W.1    Zhang, H.2
  • 4
    • 28244496090 scopus 로고    scopus 로고
    • Benchmarking optimization software with performance profiles
    • Dolan, E. D., Moré, J. J.: Benchmarking optimization software with performance profiles. Math. Program. 91, 201-213 (2002).
    • (2002) Math. Program. , vol.91 , pp. 201-213
    • Dolan, E.D.1    Moré, J.J.2
  • 5
    • 65349138571 scopus 로고    scopus 로고
    • An unconstrained optimization test functions collection
    • Andrei, N.: An unconstrained optimization test functions collection. Adv. Model. Optim. 10, 147-161 (2008).
    • (2008) Adv. Model. Optim. , vol.10 , pp. 147-161
    • Andrei, N.1
  • 6
    • 0000135303 scopus 로고
    • Methods of conjugate gradients for solving linear systems
    • Hestenes, M. R., Stiefel, E. L.: Methods of conjugate gradients for solving linear systems. J. Res. Natl. Bur. Stand. 49, 409-436 (1952).
    • (1952) J. Res. Natl. Bur. Stand. , vol.49 , pp. 409-436
    • Hestenes, M.R.1    Stiefel, E.L.2
  • 7
    • 0035730017 scopus 로고    scopus 로고
    • An efficient hybrid conjugate gradient method for unconstrained optimization
    • Dai, Y. H., Yuan, Y.: An efficient hybrid conjugate gradient method for unconstrained optimization. Ann. Oper. Res. 103, 33-47 (2001).
    • (2001) Ann. Oper. Res. , vol.103 , pp. 33-47
    • Dai, Y.H.1    Yuan, Y.2
  • 8
    • 0001903222 scopus 로고
    • Note sur la convergence de directions conjuguée
    • Polak, E., Ribière, G.: Note sur la convergence de directions conjuguée. Rev. Fr. Inf. Rech. Oper. 16, 35-43 (1969).
    • (1969) Rev. Fr. Inf. Rech. Oper. , vol.16 , pp. 35-43
    • Polak, E.1    Ribière, G.2
  • 9
    • 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, 94-112 (1969).
    • (1969) USSR Comput. Math. Math. Phys. , vol.9 , pp. 94-112
    • Polyak, B.T.1
  • 10
    • 33144465578 scopus 로고    scopus 로고
    • A new conjugate gradient method with guaranteed descent and an efficient line search
    • Hager, W. W., Zhang, H.: A new conjugate gradient method with guaranteed descent and an efficient line search. SIAM J. Optim. 16, 170-192 (2005).
    • (2005) SIAM J. Optim. , vol.16 , pp. 170-192
    • Hager, W.W.1    Zhang, H.2
  • 11
    • 33646887390 scopus 로고
    • On the limited memory BFGS method for large scale optimization methods
    • Liu, D. C., Nocedal, J.: On the limited memory BFGS method for large scale optimization methods. Math. Program. 45, 503-528 (1989).
    • (1989) Math. Program. , vol.45 , pp. 503-528
    • Liu, D.C.1    Nocedal, J.2
  • 13
    • 0014492147 scopus 로고
    • Convergence conditions for ascent methods
    • Wolfe, P.: Convergence conditions for ascent methods. SIAM Rev. 11, 226-235 (1969).
    • (1969) SIAM Rev. , vol.11 , pp. 226-235
    • Wolfe, P.1
  • 14
    • 0242529976 scopus 로고
    • A modified conjugate gradient algorithm
    • Perry, A.: A modified conjugate gradient algorithm. Oper. Res. 26, 1073-1078 (1978).
    • (1978) Oper. Res. , vol.26 , pp. 1073-1078
    • Perry, A.1
  • 15
    • 0000618748 scopus 로고
    • Conjugate gradient methods with inexact searches
    • Shanno, D. F.: Conjugate gradient methods with inexact searches. Math. Oper. Res. 3, 244-256 (1978).
    • (1978) Math. Oper. Res. , vol.3 , pp. 244-256
    • Shanno, D.F.1
  • 16
    • 0034831849 scopus 로고    scopus 로고
    • New conjugacy conditions and related nonlinear conjugate gradient methods
    • Dai, Y. H., Liao, L. Z.: New conjugacy conditions and related nonlinear conjugate gradient methods. Appl. Math. Optim. 43, 87-101 (2001).
    • (2001) Appl. Math. Optim. , vol.43 , pp. 87-101
    • Dai, Y.H.1    Liao, L.Z.2
  • 17
    • 36148998344 scopus 로고    scopus 로고
    • Scaled conjugate gradient algorithms for unconstrained optimization
    • Andrei, N.: Scaled conjugate gradient algorithms for unconstrained optimization. Comput. Optim. Appl. 38, 401-416 (2007).
    • (2007) Comput. Optim. Appl. , vol.38 , pp. 401-416
    • Andrei, N.1
  • 18
    • 34147204085 scopus 로고    scopus 로고
    • Scaled memoryless BFGS preconditioned conjugate gradient algorithm for unconstrained optimization
    • Andrei, N.: Scaled memoryless BFGS preconditioned conjugate gradient algorithm for unconstrained optimization. Optim. Methods Softw. 22, 561-571 (2007).
    • (2007) Optim. Methods Softw. , vol.22 , pp. 561-571
    • Andrei, N.1
  • 19
    • 0141467950 scopus 로고    scopus 로고
    • A spectral conjugate gradient method for unconstrained optimization
    • Birgin, E., Martínez, J. M.: A spectral conjugate gradient method for unconstrained optimization. Appl. Math. Optim. 43, 117-128 (2001).
    • (2001) Appl. Math. Optim. , vol.43 , pp. 117-128
    • Birgin, E.1    Martínez, J.M.2
  • 20
    • 21844503871 scopus 로고
    • A subspace study on conjugate gradient algorithms
    • Yuan, Y., Stoer, J.: A subspace study on conjugate gradient algorithms. Z. Angew. Math. Mech. 75, 69-77 (1995).
    • (1995) Z. Angew. Math. Mech. , vol.75 , pp. 69-77
    • Yuan, Y.1    Stoer, J.2
  • 21
    • 0016926995 scopus 로고
    • Algorithm 500. Minimization of unconstrained multivariate functions
    • Shanno, D. F., Phua, K. H.: Algorithm 500. Minimization of unconstrained multivariate functions. ACM Trans. Math. Softw. 2, 87-94 (1976).
    • (1976) ACM Trans. Math. Softw. , vol.2 , pp. 87-94
    • Shanno, D.F.1    Phua, K.H.2
  • 22
    • 67349265141 scopus 로고    scopus 로고
    • Acceleration of conjugate gradient algorithms for unconstrained optimization
    • Andrei, N.: Acceleration of conjugate gradient algorithms for unconstrained optimization. Appl. Math. Comput. 213, 361-369 (2009).
    • (2009) Appl. Math. Comput. , vol.213 , pp. 361-369
    • Andrei, N.1
  • 23
    • 0028511736 scopus 로고
    • Line search algorithms with guaranteed sufficient decrease
    • Moré, J. J., Thuente, D. J.: Line search algorithms with guaranteed sufficient decrease. ACM Trans. Math. Softw. 20, 286-307 (1994).
    • (1994) ACM Trans. Math. Softw. , vol.20 , pp. 286-307
    • Moré, J.J.1    Thuente, D.J.2
  • 25
    • 0017574977 scopus 로고
    • On a problem of the theory of lubrication governed by a variational inequality
    • Cimatti, G.: On a problem of the theory of lubrication governed by a variational inequality. Appl. Math. Optim. 3, 227-242 (1977).
    • (1977) Appl. Math. Optim. , vol.3 , pp. 227-242
    • Cimatti, G.1
  • 26
    • 0022766604 scopus 로고
    • Numerical study of a relaxed variational problem from optimal design
    • Goodman, J., Kohn, R., Reyna, L.: Numerical study of a relaxed variational problem from optimal design. Comput. Methods Appl. Mech. Eng. 57, 107-127 (1986).
    • (1986) Comput. Methods Appl. Mech. Eng. , vol.57 , pp. 107-127
    • Goodman, J.1    Kohn, R.2    Reyna, L.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.