Efficient implementation of a generalized polak-ribière algorithm for nonlinear optimization

References

• Liu , Y. and Storey , C. 1991 . Efficient generalized conjugate gradient algorithms Part 1: Theory . Journal of Optimization Theory and Applications , 69 ( 1 ) : 129 – 137 .
   Web of Science ®Google Scholar
• Hu , Y. F. and Storey , C. 1991 . Efficient generalized conjugate gradient algorithms, Part 2: Implementation . Journal of Optimization Theory and Applications , 69 ( 1 ) : 139 – 152 .
   Web of Science ®Google Scholar
• Hu Y. F. Storey C. On Unconstrained Conjugate Gradient Optimization Methods and their Interrelationships Department of Mathematical Sciences, Loughborough University of Technology Leicestershire, England July 1990 Mathematics Report No. A129
   Google Scholar
• Khoda , K. M. , Liu , Y. and Storey , C. 1992 . A generalized Polak-Ribière algorithm . Journal of Optimization Theory and Applications , 75 ( 2 ) : 345 – 354 .
   Web of Science ®Google Scholar
• Khoda K. M. A Theoretical and Computational Investigation of a Generalized Polak-Ribière Algorithm for Unconstrained Optimization Department of Mathematical Sciences, Loughborough University of Technology Loughborough, Leicestershire England February 1992 Ph.D. Thesis
   Google Scholar
• Lukšan L. Computational Experience with Improved Conjugate Gradient Methods for Unconstrained Minimization Institute of Computer and Information Science Prague February 1991 572 Technical Report No. 488
   Google Scholar
• Powell , M. J. D. 1977 . Restart procedures for the conjugate gradient methods . Mathematical Programming , 12 ( 2 ) : 241 – 254 .
   Web of Science ®Google Scholar
• Shanno , D. F. 1985 . Globally convergent conjugate gradient algorithms . Mathematical Programming , 33 ( 2 ) : 61 – 67 .
   Web of Science ®Google Scholar
• Touati-Ahmed , D. and Storey , C. 1990 . Efficient hybrid conjugate gradient techniques . Journal of Optimization Theory and Applications , 64 ( 2 ) : 379 – 397 .
   Web of Science ®Google Scholar
• Nazareth , L. 1977 . A conjugate direction algorithm without line searches . Journal of Optimization Theory and Applications , 23 ( 3 ) : 373 – 387 .
   Web of Science ®Google Scholar
• Dixon L. C. W. Ducksbury P. G. Singh P. A New Three Term Conjugate Gradient Method Numerical Optimization Centre, The Hatfield Polytechnic Hatfield, Hertforshire, England 1985 Technical Report No. 130
   Google Scholar
• Beale , E. M. L. 1972 . “ Numerical Methods for Nonlinear Optimization ” . In A Derivation of Conjugate Gradients , Edited by: Lootsma , F. A. 39 – 43 . England : Academic Press .
   Google Scholar
• Gilbert J. C. Nocedal J. Global Convergence Properties of Conjugate Gradient Methods for Optimization Institut National de Recherche en Informatique et en Automatique Le Chesnay Cedex, France June 1990 Rapport de Recherche No. 1268, , Domaine de Voluceau, Rocquencourt, B.P.105, 78153
   Google Scholar
• Hu , Y. F. and Storey , C. 1991 . A global convergence result for conjugate gradient methods . Journal of Optimization Theory and Applications , 71 ( 2 ) : 399 – 405 .
   Web of Science ®Google Scholar
• Liu Y. M Private Communication April 1990
   Google Scholar
• Fletcher , R. 1987 . Practical Methods of Optimization , England : John Wiley & Sons .
   Google Scholar
• Nocedal , J. 1980 . Updating quasi-Newton matrices with limited storage . Mathematics of Computation , 35 ( 151 ) : 773 – 782 .
   Web of Science ®Google Scholar
• Buckley , A. and Le Nir , A. 1983 . QN-like variable storage conjugate gradients . Mathematical Programming , 27 ( 2 ) : 155 – 175 .
   Web of Science ®Google Scholar
• Buckley , A. and Le Nir , A. 1985 . Algorithm 630: BBVSCG—A variable storage algorithm for function minimization . ACM Transactions on Mathematical Software , 11 ( 2 ) : 103 – 119 .
   Web of Science ®Google Scholar
• Shanno , D. F. 1978 . Conjugate gradient methods with inexact searches . Mathematics of Operations Research , 3 ( 3 ) : 244 – 256 .
   Google Scholar
• Shanno , D. F. and Phua , K. M. 1980 . Remark on algorithm 500: minimization of unconstrained multivariate functions . ACM Transactions on Mathematical Software , 6 ( 4 ) : 618 – 622 .
   Google Scholar
• Liu , D. C. and Nocedal , J. 1989 . On the limited memory BFGS method for large scale optimization . Mathematical Programming , 45 ( 4 ) : 503 – 528 .
   Web of Science ®Google Scholar