A modified Polak–Ribière–Polyak conjugate gradient algorithm for unconstrained optimization

References

• Andrei , N . 2006 . An acceleration of gradient descent algorithm with backtracking for unconstrained optimization . Numer. Algorithms , 42 : 63 – 73 .
   Web of Science ®Google Scholar
• Andrei , N . 2007 . Scaled conjugate gradient algorithms for unconstrained optimization . Comput. Optim. Appl. , 38 : 401 – 416 .
   Web of Science ®Google Scholar
• Andrei , N . 2007 . Scaled memoryless BFGS preconditioned conjugate gradient algorithm for unconstrained optimization . Optim. Methods Softw. , 22 : 561 – 571 .
   Web of Science ®Google Scholar
• Andrei , N . 2007 . Numerical comparison of conjugate gradient algorithms for unconstrained optimization . Stud. Inf. Control , 16 : 333 – 352 .
   Google Scholar
• Andrei , N . 2008 . An unconstrained optimization test functions collection . Adv. Model. Optim. , 10 : 147 – 161 .
   Google Scholar
• Andrei , N . 2009 . Acceleration of conjugate gradient algorithms for unconstrained optimization . Appl. Math. Comput. , 213 : 361 – 369 .
   Web of Science ®Google Scholar
• Beale , EML . 1972 . “ A derivative of conjugate gradients ” . In Numerical Methods for Nonlinear Optimization , Edited by: Lootsma , FA . 39 – 43 . London : Academic Press .
   Google Scholar
• Dai , YH . Analyses of conjugate gradient methods, Ph.D. Thesis, Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, 1997
   Google Scholar
• Dai , YH and Liao , LZ . 2001 . New conjugate conditions and related nonlinear conjugate gradient methods . Appl. Math. Optim. , 43 : 87 – 101 .
   Web of Science ®Google Scholar
• Dai , YH , Liao , LZ and Li , D . 2004 . On restart procedures for the conjugate gradient method . Numer. Algorithms , 35 : 249 – 260 .
   Web of Science ®Google Scholar
• Dai , YH and Yuan , Y . 1999 . Convergence of three-term conjugate gradient methods . Math. Numer. Sin. , 21 : 355 – 362 . Translated in Chinese J. Numer. Math. Appl. 21 (1999), pp. 69–78
   Google Scholar
• Dai , YH 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
• Fletcher , R . Practical Methods of Optimization, Vol. 1: Unconstrained Optimization, John Wiley & Sons, New York, 1987
   Google Scholar
• Fletcher , R and Reeves , CM . 1964 . Function minimization by conjugate gradients . Comput. J. , 7 : 149 – 154 .
   Web of Science ®Google Scholar
• Gilbert , JC and Nocedal , J . 1992 . Global convergence properties of conjugate gradient methods for optimization . SIAM J. Optim. , 2 : 21 – 42 .
   Web of Science ®Google Scholar
• Hestenes , MR and Stiefel , EL . 1952 . Methods of conjugate gradients for solving linear systems . J. Research Nat. Bur. Standards , 49 : 409 – 436 .
   Google Scholar
• Liu , DC and Nocedal , J . 1989 . On the limited memory BFGS method for large scale optimization methods . Math. Program , 45 : 503 – 528 .
   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
• Luenberger , D . 1973 . Introduction to Linear and Nonlinear Programming , Reading, MA : Addison-Wesley .
   Google Scholar
• Nazareth , L . 1977 . A conjugate direction algorithm without line search . J. Optim. Theory Appl. , 23 : 373 – 387 .
   Web of Science ®Google Scholar
• Nocedal , J . 1996 . “ Conjugate gradient methods and nonlinear optimization ” . In Linear and Nonlinear Conjugate Gradient Related Methods , Edited by: Adams , L and Nazareth , JL . 9 – 23 . Philadelphia : SIAM .
   Google Scholar
• Polak , E and Ribière , G . 1969 . Note sur la convergence de directions conjuguée . Rev. Francaise Informat Recherche Operationelle, 3e Année , 16 : 35 – 43 .
   Google Scholar
• Polyak , BT . 1969 . The conjugate gradient method in extreme problems . USSR Comp. Math. Math. Phys. , 9 : 94 – 112 .
   Google Scholar
• Powell , MJD . 1977 . Restart procedures of the conjugate gradient method . Math. Program. , 2 : 241 – 254 .
   Web of Science ®Google Scholar
• Powell , MJD . 1983 . Nonconvex minimization calculations and the conjugate gradient method , Dundee : in Numerical Analysis . Lecture Notes in Mathematics, Vol. 1066, Springer, Berlin, 1984, pp. 122–141
   Google Scholar
• Shanno , DF and Phua , KH . 1976 . Algorithm 500, Minimization of unconstrained multivariate functions . ACM Trans. Math. Soft. , 2 : 87 – 94 .
   Google Scholar
• Yuan , Y-X . 1993 . Analysis on the conjugate gradient method . Optim. Methods Softw. , 2 : 19 – 29 .
   Google Scholar
• Zhang , J , Xiao , Y and Wei , Z . 2009 . Nonlinear conjugate gradient methods with sufficient descent condition for large-scale unconstrained optimization . Math. Prob. Eng. , 2009 Article ID 243290, 16 pp. DOI: 10.1155/2009/243290
   Web of Science ®Google Scholar
• Zhang , L , Zhou , W and Li , DH . 2006 . A descent modified Polak–Ribière–Polyak conjugate gradient method and its global convergence . IMA J. Numer. Anal. , 26 : 629 – 640 .
   Web of Science ®Google Scholar