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Volumn 92, Issue , 2015, Pages 70-81

A three-term conjugate gradient algorithm for large-scale unconstrained optimization problems

Author keywords

Algorithm; Global convergence; Inexact line search; Large scale problems; Three term conjugate gradient method

Indexed keywords

BENCHMARKING; CONJUGATE GRADIENT METHOD; GRADIENT METHODS; ITERATIVE METHODS; OPTIMIZATION;

EID: 84923261681     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2015.01.008     Document Type: Article
Times cited : (38)

References (36)
  • 1
    • 84923224435 scopus 로고    scopus 로고
    • A global convergent spectral conjugate gradient method
    • A.Y. Al-Bayati, and Hawraz N. Al-khayat A global convergent spectral conjugate gradient method Aust. J. Basic Appl. Sci. 7 2013 303 309
    • (2013) Aust. J. Basic Appl. Sci. , vol.7 , pp. 303-309
    • Al-Bayati, A.Y.1    Al-Khayat, H.N.2
  • 2
    • 84869084756 scopus 로고    scopus 로고
    • A new three-term conjugate gradient method for unconstrained optimization
    • A.Y. Al-Bayati, and W.H. Sharif A new three-term conjugate gradient method for unconstrained optimization Can. J. Sci. Eng. Math. 1 2010 108 124
    • (2010) Can. J. Sci. Eng. Math. , vol.1 , pp. 108-124
    • Al-Bayati, A.Y.1    Sharif, W.H.2
  • 3
    • 65349138571 scopus 로고    scopus 로고
    • An unconstrained optimization test functions collection
    • N. Andrei An unconstrained optimization test functions collection Adv. Model. Optim. 10 2008 147 161
    • (2008) Adv. Model. Optim. , vol.10 , pp. 147-161
    • Andrei, N.1
  • 4
    • 67349265141 scopus 로고    scopus 로고
    • Acceleration of conjugate gradient algorithm for unconstrained optimization
    • N. Andrei Acceleration of conjugate gradient algorithm for unconstrained optimization Appl. Math. Comput. 213 2009 361 369
    • (2009) Appl. Math. Comput. , vol.213 , pp. 361-369
    • Andrei, N.1
  • 5
    • 84858131937 scopus 로고    scopus 로고
    • A modified Polak-Ribière-Polyak conjugate gradient algorithm for unconstrained optimization
    • N. Andrei A modified Polak-Ribière-Polyak conjugate gradient algorithm for unconstrained optimization Optimization 60 2011 1457 1471
    • (2011) Optimization , vol.60 , pp. 1457-1471
    • Andrei, N.1
  • 6
    • 84867746781 scopus 로고    scopus 로고
    • A simple three-term conjugate gradient algorithm for unconstrained optimization
    • N. Andrei A simple three-term conjugate gradient algorithm for unconstrained optimization J. Comput. Appl. Math. 241 2013 19 29
    • (2013) J. Comput. Appl. Math. , vol.241 , pp. 19-29
    • Andrei, N.1
  • 7
    • 84872919695 scopus 로고    scopus 로고
    • On three-term conjugate gradient algorithms for unconstrained optimization
    • N. Andrei On three-term conjugate gradient algorithms for unconstrained optimization Appl. Math. Comput. 219 2013 6316 6327
    • (2013) Appl. Math. Comput. , vol.219 , pp. 6316-6327
    • Andrei, N.1
  • 8
    • 84884514636 scopus 로고    scopus 로고
    • Another conjugate gradient algorithm with guaranteed descent and conjugacy conditions
    • N. Andrei Another conjugate gradient algorithm with guaranteed descent and conjugacy conditions J. Optim. Theory Appl. 159 1 2013 159 182 10.1007/s10957-013-0285-9
    • (2013) J. Optim. Theory Appl. , vol.159 , Issue.1 , pp. 159-182
    • Andrei, N.1
  • 9
    • 0010515793 scopus 로고
    • A derivation of conjugate gradients
    • F.A. Lootsma, Academic Press London
    • E.M.L. Beale A derivation of conjugate gradients F.A. Lootsma, Numerical Methods for Nonlinear Optimization 1972 Academic Press London 39 43
    • (1972) Numerical Methods for Nonlinear Optimization , pp. 39-43
    • Beale, E.M.L.1
  • 10
    • 0000024679 scopus 로고
    • CUTE: Constrained and unconstrained testing environment
    • I. Bongartz, and A.R. Conn CUTE: constrained and unconstrained testing environment ACM Trans. Math. Softw. 21 1 March 1995 124 160
    • (1995) ACM Trans. Math. Softw. , vol.21 , Issue.1 , pp. 124-160
    • Bongartz, I.1    Conn, A.R.2
  • 11
    • 37549018121 scopus 로고    scopus 로고
    • A two-term PRP-based descent method
    • W. Cheng A two-term PRP-based descent method Numer. Funct. Anal. Optim. 28 2007 1217 1230
    • (2007) Numer. Funct. Anal. Optim. , vol.28 , pp. 1217-1230
    • Cheng, W.1
  • 12
    • 0010846477 scopus 로고
    • Linear convergence of the conjugate gradient method
    • H.P. Crowder, and P. Wolfe Linear convergence of the conjugate gradient method IBM J. Res. Dev. 16 1969 431 433
    • (1969) IBM J. Res. Dev. , vol.16 , pp. 431-433
    • Crowder, H.P.1    Wolfe, P.2
  • 13
    • 17644432398 scopus 로고    scopus 로고
    • Convergence properties of the Beale-Powell restart algorithm
    • Y.H. Dai, and Y. Yuan Convergence properties of the Beale-Powell restart algorithm Sci. China Ser. A 41 1998 1142 1150
    • (1998) Sci. China Ser. A , vol.41 , pp. 1142-1150
    • Dai, Y.H.1    Yuan, Y.2
  • 14
    • 0033266804 scopus 로고    scopus 로고
    • A nonlinear conjugate gradient method with a strong global convergence property
    • Y.H. Dai, and Y. Yuan A nonlinear conjugate gradient method with a strong global convergence property SIAM J. Optim. 10 1999 177 182
    • (1999) SIAM J. Optim. , vol.10 , pp. 177-182
    • Dai, Y.H.1    Yuan, Y.2
  • 15
    • 0035611321 scopus 로고    scopus 로고
    • A three-parameter family of nonlinear conjugate gradient methods
    • Y.H. Dai, and Y. Yuan A three-parameter family of nonlinear conjugate gradient methods Math. Comput. 70 2000 1155 1167
    • (2000) Math. Comput. , vol.70 , pp. 1155-1167
    • Dai, Y.H.1    Yuan, Y.2
  • 16
    • 84876847748 scopus 로고    scopus 로고
    • An improved spectral conjugate gradient algorithm for nonconvex unconstrained optimization problems
    • S.H. Deng, Z. Wan, and X.H. Chen An improved spectral conjugate gradient algorithm for nonconvex unconstrained optimization problems J. Optim. Theory Appl. 157 2013 820 842
    • (2013) J. Optim. Theory Appl. , vol.157 , pp. 820-842
    • Deng, S.H.1    Wan, Z.2    Chen, X.H.3
  • 17
    • 28244496090 scopus 로고    scopus 로고
    • Benchmarking optimization software with performance profiles
    • E.D. Dolan, and J.J. Moré 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
  • 18
    • 0000615669 scopus 로고
    • Function minimization by conjugate gradients
    • R. Fletcher, and C.M. Reeves Function minimization by conjugate gradients Comput. J. 7 1964 149 154
    • (1964) Comput. J. , vol.7 , pp. 149-154
    • Fletcher, R.1    Reeves, C.M.2
  • 19
    • 33144465578 scopus 로고    scopus 로고
    • A new conjugate gradient method with guaranteed descent and an efficient line search
    • W.W. Hager, and H. Zhang A new conjugate gradient method with guaranteed descent and an efficient line search SIAM J. Control Optim. 16 2005 170 192
    • (2005) SIAM J. Control Optim. , vol.16 , pp. 170-192
    • Hager, W.W.1    Zhang, H.2
  • 20
    • 33745245573 scopus 로고    scopus 로고
    • Algorithm 851: CG-DESCENT, a conjugate gradient method with guaranteed descent
    • W.W. Hager, and H. Zhang Algorithm 851: CG-DESCENT, a conjugate gradient method with guaranteed descent ACM Trans. Math. Softw. 32 2006 113 137
    • (2006) ACM Trans. Math. Softw. , vol.32 , pp. 113-137
    • Hager, W.W.1    Zhang, H.2
  • 21
    • 0000135303 scopus 로고
    • Methods of conjugate gradients for solving linear systems
    • M.R. Hestenes, and E.L. Stiefel Methods of conjugate gradients for solving linear systems J. Res. Natl. Bur. Stand. 49 6 1952 409 436
    • (1952) J. Res. Natl. Bur. Stand. , vol.49 , Issue.6 , pp. 409-436
    • Hestenes, M.R.1    Stiefel, E.L.2
  • 22
    • 84923227434 scopus 로고    scopus 로고
    • Global convergence of a modified PRP conjugate gradient method
    • H.D. Huang, Y.J. Li, and Z.X. Wei Global convergence of a modified PRP conjugate gradient method J. Math. Res. Expo. 30 2010 141 148
    • (2010) J. Math. Res. Expo. , vol.30 , pp. 141-148
    • Huang, H.D.1    Li, Y.J.2    Wei, Z.X.3
  • 23
    • 84880551560 scopus 로고    scopus 로고
    • A modified projected conjugate gradient method for unconstrained optimization problems
    • S. Huang, Z. Wan, and S.H. Deng A modified projected conjugate gradient method for unconstrained optimization problems ANZIAM J. 54 03 2013 143 152
    • (2013) ANZIAM J. , vol.54 , Issue.3 , pp. 143-152
    • Huang, S.1    Wan, Z.2    Deng, S.H.3
  • 24
    • 84923229554 scopus 로고    scopus 로고
    • Global convergence of a kind of conjugate gradient method
    • C. Li, L. Fang, and X.L. Cao Global convergence of a kind of conjugate gradient method TELKOMNIKA 11 2013 544 549
    • (2013) TELKOMNIKA , vol.11 , pp. 544-549
    • Li, C.1    Fang, L.2    Cao, X.L.3
  • 25
    • 0000659410 scopus 로고    scopus 로고
    • A conjugate direction algorithm without line search
    • L. Nazareth A conjugate direction algorithm without line search J. Optim. Theory Appl. 23 1997 373 387
    • (1997) J. Optim. Theory Appl. , vol.23 , pp. 373-387
    • Nazareth, L.1
  • 26
    • 33846446220 scopus 로고
    • Restart procedures of the conjugate gradient method
    • M.J.D. Powell Restart procedures of the conjugate gradient method Math. Program. 2 1977 241 254
    • (1977) Math. Program. , vol.2 , pp. 241-254
    • Powell, M.J.D.1
  • 27
    • 84905106012 scopus 로고    scopus 로고
    • A modified nonmonotone BFGS algorithm for solving smooth nonlinear equations
    • Z. Wan, Y. Chen, S. Huang, and D. Feng A modified nonmonotone BFGS algorithm for solving smooth nonlinear equations Optim. Lett. 8 6 2014 1845 1860
    • (2014) Optim. Lett. , vol.8 , Issue.6 , pp. 1845-1860
    • Wan, Z.1    Chen, Y.2    Huang, S.3    Feng, D.4
  • 28
    • 80155207308 scopus 로고    scopus 로고
    • A spectral PRP conjugate gradient methods for nonconvex optimization problem based on modified line search
    • Z. Wan, C.M. Hu, and Z.L. Yang A spectral PRP conjugate gradient methods for nonconvex optimization problem based on modified line search Discrete Contin. Dyn. Syst.; Ser. B 16 4 2011 1153 1169
    • (2011) Discrete Contin. Dyn. Syst.; Ser. B , vol.16 , Issue.4 , pp. 1153-1169
    • Wan, Z.1    Hu, C.M.2    Yang, Z.L.3
  • 29
    • 84873385635 scopus 로고    scopus 로고
    • New cautious BFGS algorithm based on modified Armijo-type line search
    • Z. Wan, S. Huang, and X.D. Zheng New cautious BFGS algorithm based on modified Armijo-type line search J. Inequal. Appl. 2012 2012 241 10.1186/1029-242X-2012-241
    • (2012) J. Inequal. Appl. , vol.2012 , pp. 241
    • Wan, Z.1    Huang, S.2    Zheng, X.D.3
  • 30
    • 84893576045 scopus 로고    scopus 로고
    • New BFGS method for unconstrained optimization problem based on modified Armijo line search
    • Z. Wan, K.L. Teo, X.L. Shen, and C.M. Hu New BFGS method for unconstrained optimization problem based on modified Armijo line search Optimization 63 2 2014 285 304
    • (2014) Optimization , vol.63 , Issue.2 , pp. 285-304
    • Wan, Z.1    Teo, K.L.2    Shen, X.L.3    Hu, C.M.4
  • 31
    • 77957595051 scopus 로고    scopus 로고
    • New spectral PRP conjugate gradient method for unconstrained optimization
    • Z. Wan, Z.L. Yang, and Y.L. Wang New spectral PRP conjugate gradient method for unconstrained optimization Appl. Math. Lett. 24 1 2011 16 22
    • (2011) Appl. Math. Lett. , vol.24 , Issue.1 , pp. 16-22
    • Wan, Z.1    Yang, Z.L.2    Wang, Y.L.3
  • 32
    • 0014492147 scopus 로고
    • Convergence conditions for ascent methods
    • P. Wolfe Convergence conditions for ascent methods SIAM Rev. 11 1968 226 235
    • (1968) SIAM Rev. , vol.11 , pp. 226-235
    • Wolfe, P.1
  • 33
    • 0001796942 scopus 로고
    • Convergence conditions for ascent methods (II): Some corrections
    • P. Wolfe Convergence conditions for ascent methods (II): some corrections SIAM Rev. 13 1971 185 188
    • (1971) SIAM Rev. , vol.13 , pp. 185-188
    • Wolfe, P.1
  • 34
    • 68949149079 scopus 로고    scopus 로고
    • Nonlinear conjugate gradient methods with sufficient descent condition for large-scale unconstrained optimization
    • Article ID 243290
    • J. Zhang, Y. Xiao, and Z. Wei Nonlinear conjugate gradient methods with sufficient descent condition for large-scale unconstrained optimization Math. Probl. Eng. 2009 2009 10.1155/2009/234290 Article ID 243290
    • (2009) Math. Probl. Eng. , vol.2009
    • Zhang, J.1    Xiao, Y.2    Wei, Z.3
  • 35
    • 33749621811 scopus 로고    scopus 로고
    • A descent modified Polak-Ribière-Polyak conjugate gradient method and its global convergence
    • L. Zhang, W. Zhou, and D.H. Li A descent modified Polak-Ribière-Polyak conjugate gradient method and its global convergence IMA J. Numer. Anal. 26 2006 629 640
    • (2006) IMA J. Numer. Anal. , vol.26 , pp. 629-640
    • Zhang, L.1    Zhou, W.2    Li, D.H.3
  • 36
    • 34147202932 scopus 로고    scopus 로고
    • Some descent three-term conjugate gradient methods and their global convergence
    • L. Zhang, W. Zhou, and D.H. Li Some descent three-term conjugate gradient methods and their global convergence Optim. Methods Softw. 22 2007 697 711
    • (2007) Optim. Methods Softw. , vol.22 , pp. 697-711
    • Zhang, L.1    Zhou, W.2    Li, D.H.3


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