Computational experience with improved conjugate gradient methods for unconstrained minimization

Ladislav Lukšan

Kybernetika (1992)

  • Volume: 28, Issue: 4, page 249-262
  • ISSN: 0023-5954

How to cite

top

Lukšan, Ladislav. "Computational experience with improved conjugate gradient methods for unconstrained minimization." Kybernetika 28.4 (1992): 249-262. <http://eudml.org/doc/27963>.

@article{Lukšan1992,
author = {Lukšan, Ladislav},
journal = {Kybernetika},
keywords = {restart procedures; conjugate gradient methods},
language = {eng},
number = {4},
pages = {249-262},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Computational experience with improved conjugate gradient methods for unconstrained minimization},
url = {http://eudml.org/doc/27963},
volume = {28},
year = {1992},
}

TY - JOUR
AU - Lukšan, Ladislav
TI - Computational experience with improved conjugate gradient methods for unconstrained minimization
JO - Kybernetika
PY - 1992
PB - Institute of Information Theory and Automation AS CR
VL - 28
IS - 4
SP - 249
EP - 262
LA - eng
KW - restart procedures; conjugate gradient methods
UR - http://eudml.org/doc/27963
ER -

References

top
  1. M. Al-Bali, Descent property and global convergence of the Fletcher-Reeves method with inexact line search, IMA J. Numer. Anal. 5 (1985), 121-124. (1985) MR0777963
  2. P. Baptist, J. Stoer, On the relation between quadratic termination and convergence properties of minimization algorithms, Part 2. Applications. Numer. Math. 28 (1977), 367-391. (1977) Zbl0366.65028MR0496671
  3. P. Bjorstadt, J. Nocedal, Analysis of a new algorithm for one-dimensional minimization, Computing 22 (1979), 93-100. (1979) MR0620386
  4. A. R. Conn N. I. M. Gould, P. L. Toint, Testing a class of methods for solving minimization problems with simple bounds on the variables, Math. Comp. 50 (1988), 399-430. (1988) MR0929544
  5. W.C. Davidon, Variable metric method for minimization, A.E.C. Research and Development Report ANL-5990, 1959. (1959) 
  6. W.C. Davidon, Optimally conditioned optimization algorithms without line searches, Math. Pro- gramming 9 (1975), 1-30. (1975) Zbl0328.90055MR0383741
  7. R. S. Dembo, T. Steihaug, Truncated-Newton algorithms for large-scale unconstrained minimization, Math. Programming 26 (1983), 190-212. (1983) MR0700647
  8. R. Fletcher, A FORTRAN subroutine for minimization by the method of conjugate gradients, Report No. AERE-R7073, Atomic Energy Research Establishment, Harwell 1972. (1972) 
  9. R. Fletcher, M.J. D. Powell, A rapidly convergent descent method for minimization, Computer J. 6 (1963), 163-168. (1963) Zbl0132.11603MR0152116
  10. R. Fletcher, CM. Reeves, Function minimization by conjugate gradients, Computer J. 7 (1964), 149-154. (1964) Zbl0132.11701MR0187375
  11. J.C. Gilbert, and J. Nocedal, Global convergence properties of conjugate gradient methods for optimization, Report No. 1268, Institut National de Recherche en Inforrnatique et. en Automatique, 1990. (1990) 
  12. A. Griewank, P. L. Toint, Partitioned variable metric updates for large structured optimization problems, Numer. Math. 39 (1982), 119-137. (1982) Zbl0482.65035MR0664541
  13. M. R. Hestenes, CM. Stiefel, Methods of conjugate gradient for solving linear systems, J. Res. Nat. Bur. Standards 49 (1964), 409-436. (1964) MR0060307
  14. Y. F. Hu, C. Storey, A Global Convergence Result for Conjugate Gradient Methods, Report No. A134, Loughborough University of Technology, 1990. (1990) MR1131466
  15. K.M. Khoda Y. Liu, C. Storey, A Generalized Polak-Ribiére Algorithm, Report No. A128, Loughborough University of Technology, 1990. (1990) 
  16. L. Lukšan, Variable Metric Methods. Unconstrained Minimization, Academia, Prague 1990. In Czech. (1990) MR1147645
  17. L. Lukšan, Computational experience with improved variable metric methods for unconstrained minimization, Kybernetika 26 (1990), 415-431. (1990) MR1079679
  18. J.J. Moré B.S. Garbow, K.E. Hillstrom, Testing unconstrained optimization software, ACM Trans. Math. Software 7 (1981), 17-41. (1981) MR0607350
  19. J. Nocedal, Updating quasi-Newton matrices with limited storage, Math. Comp. 35 (1980), 773-782. (1980) Zbl0464.65037MR0572855
  20. E. Polak, G. Ribiére, Note sur la convergence de methodes de directions conjugees, Revue Francaise Inform. Mech. Oper. 16-R1 (1969), 35-43. (1969) MR0255025
  21. M.J.D. Powell, Restart procedures of the conjugate gradient method, Math. Programming 12 (1977), 241-254. (1977) MR0478622
  22. M.J.D. Powell, Nonconvex Minimization Calculations and the Conjugate Gradient Method, Report No. DAMTP 1983/NA14, University of Cambridge, 1983. (1983) MR0760460
  23. M.J.D. Powell, Convergence Properties of Algorithms for Nonlinear Optimization, Report No. DAMPT 1985/NA1, University of Cambridge, 1985. (1985) MR0867680
  24. D. F. Shanno, Conditioning of quasi-Newton methods for function minimization, Math. Comp. 24 (1970), 647-656. (1970) MR0274029
  25. D.F. Shanno, Globally convergent conjugate gradient algorithms, Math. Programming 33 (1985), 61-67. (1985) Zbl0579.90079MR0809749
  26. P. L. Toint, On sparse and symmetric matrix updating subject to a linear equation, Math. Comp. 31 (1987), 954-961. (1987) MR0455338
  27. D. Touati-Ahmed, C. Storey, Efficient hybrid conjugate gradient techniques, J. Optim. Theory Appl. 64 (1990), 379-397. (1990) Zbl0666.90063MR1042002
  28. G. Zoutendijk, Nonlinear programming, computational methods, In: Integer and Nonlinear Programming (J. Abadie, ed.), North-Holland, Amsterdam 1970, pp. 93-121. (1970) Zbl0336.90057MR0437081

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.