An accelerated conjugate gradient algorithm with guaranteed descent and conjugacy conditions 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 . A scaled BFGS preconditioned conjugate gradient algorithm for unconstrained optimization . Appl. Math. Lett. , 20 : 645 – 650 .
   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
• Aris , R. 1975 . The mathematical theory of diffusion and reaction in permeable catalysts , Oxford : Clarendon Press .
   Google Scholar
• Averick , B. M. , Carter , R. G. , Moré , J. J. and Xue , G. L. The MINPACK-2 Test Problem Collection Mathematics and Computer Science Division, Argonne National Laboratory, Preprint MCS-P153-0692, June 1992.
   Google Scholar
• Bebernes , J. and Eberly , D. 1989 . Mathematical Problems from Combustion Theory , New York : Springer-Verlag . Applied Mathematical Sciences, Vol. 83
   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. Softw. , 21 : 123 – 160 .
   Web of Science ®Google Scholar
• Boyd , S. and Vandenberghe , L. 2004 . Convex Optimization , Cambridge : Cambridge University Press .
   Google Scholar
• Cimatti , G. 1977 . On a problem of the theory of lubrication governed by a variational inequality . Appl. Math. Optim. , 3 : 227 – 242 .
   Web of Science ®Google Scholar
• Dai , Y. H. 2001 . New properties of a nonlinear conjugate gradient method . Numer. Math. , 89 : 83 – 98 .
   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 Yuan , Y. 2001 . An efficient hybrid conjugate gradient method for unconstrained optimization, . Ann. Oper. 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
• Dolan , E. D. and Moré , J. J. 2002 . Benchmarking optimization software with performance profiles . Math. Program. , 91 : 201 – 213 .
   Web of Science ®Google Scholar
• Fletcher , R. 1980 . Practical Optimization: Vol. 1: Unconstrained Optimization , Chichester : John Wiley and 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
• Glowinski , R. 1984 . Numerical Methods for Nonlinear Variational Problems , Berlin : Springer-Verlag .
   Google Scholar
• Goodman , J. , Kohn , R. and Reyna , L. 1986 . Numerical study of a relaxed variational problem from optimal design . Comput. Methods Appl. Mech. Eng. , 57 : 107 – 127 .
   Web of Science ®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. L. 1952 . Methods of conjugate gradients for solving linear systems . J. Res. Nat. Bur. Stand. , 49 : 409 – 436 .
   Google Scholar
• Li , G. , Tang , C. and Wei , Z. 2007 . New conjugacy condition and related new conjugate gradient methods for unconstrained optimization . J. Comput. Appl. Math. , 202 : 523 – 539 .
   Web of Science ®Google Scholar
• Liu , D. C. 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
• Nitsche , J. C.C. 1989 . Lectures on Minimal Surfaces , Vol. 1 , New York : Cambridge University Press .
   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 , J. L. 9 – 23 . Philadelphia : SIAM .
   Google Scholar
• Perry , A. 1978 . A modified conjugate gradient algorithm . Oper. Res. , 26 : 1073 – 1078 .
   Web of Science ®Google Scholar
• Polak , E. 1971 . Computational methods in optimization: A unified approach , New York : Academic Press .
   Google Scholar
• Polak , E. and Ribière , G. 1969 . Note sur la convergence de directions conjuguée, . Rev. Fr. Inform. Rech. Oper. 3e Année , 16 : 35 – 43 .
   Google Scholar
• Polyak , B. T. 1969 . The conjugate gradient method in extreme problems . USSR Comp. Math. Math. Phys. , 9 : 94 – 112 .
   Google Scholar
• Powell , M. J.D. 1976 . Some convergence properties of the conjugate gradient method . Math. Program. , 11 : 42 – 49 .
   Web of Science ®Google Scholar
• Powell , M. J.D. 1984 . “ Nonconvex minimization calculations and the conjugate gradient method ” . In Numerical Analysis , 122 – 141 . Berlin : Springer-Verlag . Dundee, 1983, Lecture Notes in Mathematics, Vol. 1066
   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. Softw. , 2 : 87 – 94 .
   Google Scholar
• Yuan , Y. 1990 . Analysis on the conjugate gradient method , China : Computing Center, Academia Sinica . Technical Report
   Google Scholar
• Yuan , Y. and Stoer , J. 1995 . A subspace study on conjugate gradient algorithms . Z. Angew. Math. Mech. , 75 : 69 – 77 .
   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
• Zoutendijk , G. 1970 . “ Nonlinear programming computational methods ” . In Integer and Nonlinear Programming , Edited by: Abadie , J. 37 – 86 . Amsterdam : North-Holland .
   Google Scholar