Another nonlinear conjugate gradient algorithm for unconstrained optimization

References

• Andrei , N. 2005 . Conjugate gradient algorithms for large scale unconstrained optimization . ICI Tech. Rep. , 12 January
   Google Scholar
• Andrei , N. 2007 . Scaled conjugate gradient algorithms for unconstrained optimization . Comput. Optim. Appl. , 38 ( 3 ) : 401 – 416 .
   Web of Science ®Google Scholar
• Andrei , N. 2007 . Scaled memoryless BFGS preconditioned conjugate gradient algorithm for unconstrained optimization . Optim. Methods Software , 22 ( 4 ) August : 561 – 571 .
   Web of Science ®Google Scholar
• Andrei , N. 2007 . A scaled BFGS preconditioned conjugate gradient algorithm for unconstrained optimization . Appl. Math. Lett. , 20 : 645 – 650 .
   Web of Science ®Google Scholar
• Andrei , N. 2008 . An unconstrained optimization test functions collection . Adv. Model. Optim. An Electr. Int. J. , 10 : 147 – 161 .
   Google Scholar
• Birgin , E. and Martínez , J. M. 2001 . A spectral conjugate gradient method for unconstrained optimization . Appl. Math. Optim. , 43 : 117 – 128 .
   Web of Science ®Google Scholar
• Bongartz , I. , Conn , A. R. , Gould , N. I.M. and Toint , P. L. 1995 . CUTE: constrained and unconstrained testing environments . ACM Trans. Math. Software , 21 : 123 – 160 .
   Web of Science ®Google Scholar
• Dai , Y. H. and Liao , L. Z. 2001 . New conjugacy conditions and related nonlinear conjugate gradient methods . Appl. Math. Optim. , 43 : 87 – 101 .
   Web of Science ®Google Scholar
• Dai , Y. H. and Ni , Q. 2003 . Testing different conjugate gradient methods for large-scale unconstrained optimization . J. Comput. Math. , 21 : 311 – 320 .
   Web of Science ®Google Scholar
• Dai , Y. H. and Yuan , Y. 1999 . A nonlinear conjugate gradient method with a strong global convergence property . SIAM J. Optim. , 10 : 177 – 182 .
   Web of Science ®Google Scholar
• Dai , Y. H. and Yuan , Y. 2001 . An efficient hybrid conjugate gradient method for unconstrained optimization . Ann. Operat. Res. , 103 : 33 – 47 .
   Web of Science ®Google Scholar
• Dai , Y. H. , Han , J. Y. , Liu , G. H. , Sun , D. F. , Yin , X. and Yuan , Y. 1999 . Convergence properties of nonlinear conjugate gradient methods . SIAM J. Optim. , 10 : 348 – 358 .
   Web of Science ®Google Scholar
• Fletcher , R. 1987 . Practical Methods of Optimization, Vol.1: Unconstrained Optimization , New York : John Wiley & Sons .
   Google Scholar
• Fletcher , R. and Reeves , C. M. 1964 . Function minimization by conjugate gradients . Comput. J. , 7 : 149 – 154 .
   Web of Science ®Google Scholar
• Gilbert , J. C. and Nocedal , J. 1992 . Global convergence properties of conjugate gradient methods for optimization . SIAM J. Optim. , 2 : 21 – 42 .
   Web of Science ®Google Scholar
• Golub , G. H. and O'Leary , D. P. 1976 . Some history of the conjugate gradient and Lanczos algorithms: 1948–1976 . SIAM Rev. , 31 : 50 – 100 .
   Google Scholar
• Hager , W. W. and Zhang , H. 2005 . A new conjugate gradient method with guaranteed descent and an efficient line search . SIAM J. Optim. , 16 : 170 – 192 .
   Web of Science ®Google Scholar
• Hager , W. W. and Zhang , H. 2006 . A survey of nonlinear conjugate gradient methods . Pacific J. Optim. , 2 : 35 – 58 .
   Google Scholar
• Hestenes , M. R. and Stiefel , E. 1952 . Methods of conjugate gradients for solving linear systems . J. Res. Nat. Bur. Standards Sec. B , 48 : 409 – 436 .
   Google Scholar
• Hu , Y. F. and Storey , C. 1991 . Global convergence result for conjugate gradient methods . JOTA , 71 : 399 – 405 .
   Web of Science ®Google Scholar
• Liu , Y. and Storey , C. 1991 . Efficient generalized conjugate gradient algorithms, Part 1: Theory . JOTA , 69 : 129 – 137 .
   Web of Science ®Google Scholar
• Nocedal , J. 1992 . Theory of algorithms for unconstrained optimization . Acta Numer. , 1 : 199 – 242 .
   Google Scholar
• O'Leary , D. P. 1996 . “ Conjugate gradients and related KMP algorithms: the beginnings ” . In Linear and Nonlinear Conjugate Gradient – Related Methods , Edited by: Adams , L. and Nazareth , J. L. 1 – 8 . Philadelphia : SIAM .
   Google Scholar
• Perry , J. M. 1977 . “ A class of conjugate gradient algorithms with a two-step variable-metric memory ” . Evanston, Illinois : Center for Mathematical Studies in Economic and Management Sciences, Northwestern University . Discussion Paper 269
   Google Scholar
• Polyak , B. T. 1969 . The conjugate gradient method in extreme problems . USSR Comp. Math. Math. Phys. , 9 : 94 – 112 .
   Google Scholar
• Polak , E. and Ribière , G. 1969 . Note sur la convergence de méthodes de directions conjuguée . 16 : 35 – 43 . Revue Francaise Informat. Recherche Opérationnelle, 3e Année
   Google Scholar
• Powell , M. J.D. 1984 . “ Nonconvex minimization calculations and the conjugate gradient method ” . Lecture Notes in Mathematics, vol. 1066 122 – 141 . Berlin : Springer Verlag . Numerical Analysis (Dundee, 1983)
   Google Scholar
• Shanno , D. F. 1978 . On the convergence of a new conjugate gradient algorithm . SIAM J. Numer. Anal. , 15 : 1247 – 1257 .
   Web of Science ®Google Scholar
• Shanno , D. F. 1978 . Conjugate gradient methods with inexact searches . Math. Oper. Res. , 3 : 244 – 256 .
   Google Scholar
• Shanno , D. F. and Phua , K. H. 1976 . Algorithm 500, Minimization of unconstrained multivariate functions . ACM Trans. Math. Soft. , 2 : 87 – 94 .
   Google Scholar
• Touati-Ahmed , D. and Storey , C. 1990 . Efficient hybrid conjugate gradient techniques . J. Optim. Theor. Appl. , 64 : 379 – 397 .
   Web of Science ®Google Scholar
• Wolfe , P. 1969 . Convergence conditions for ascent methods . SIAM Rev. , 11 : 226 – 235 .
   Web of Science ®Google Scholar
• Wolfe , P. 1971 . Convergence conditions for ascent methods, (II): some corrections . SIAM Rev. , 13 : 185 – 188 .
   Web of Science ®Google Scholar
• Yu , G. , Guan , L. and Chen , W. 2008 . Spectral conjugate gradient methods with sufficient descent property for large-scale unconstrained optimization . Optim. Methods and Software , 23 ( 2 ) : 275 – 293 .
   Web of Science ®Google Scholar