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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 986317, 6 pages
http://dx.doi.org/10.1155/2013/986317
Research Article

A Conjugate Gradient Type Method for the Nonnegative Constraints Optimization Problems

College of Mathematics, Honghe University, Mengzi 661199, China

Received 16 December 2012; Accepted 20 March 2013

Academic Editor: Theodore E. Simos

Copyright © 2013 Can Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. R. Hestenes and E. Stiefel, “Methods of conjugate gradients for solving linear systems,” Journal of Research of the National Bureau of Standards, vol. 49, pp. 409–436, 1952. View at Zentralblatt MATH · View at MathSciNet
  2. R. Fletcher and C. M. Reeves, “Function minimization by conjugate gradients,” The Computer Journal, vol. 7, pp. 149–154, 1964. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. B. Polak and G. Ribire, “Note sur la convergence de directions conjugees,” Revue Française d'Informatique et de Recherche Opérationnelle, vol. 16, pp. 35–43, 1969.
  4. B. T. Polyak, “The conjugate gradient method in extremal problems,” USSR Computational Mathematics and Mathematical Physics, vol. 9, no. 4, pp. 94–112, 1969. View at Scopus
  5. R. Fletcher, Practical Methods of Optimization, John Wiley & Sons Ltd., Chichester, UK, 2nd edition, 1987. View at MathSciNet
  6. Y. Liu and C. Storey, “Efficient generalized conjugate gradient algorithms. I. Theory,” Journal of Optimization Theory and Applications, vol. 69, no. 1, pp. 129–137, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. Y. H. Dai and Y. Yuan, “A nonlinear conjugate gradient method with a strong global convergence property,” SIAM Journal on Optimization, vol. 10, no. 1, pp. 177–182, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. M. J. D. Powell, “Convergence properties of algorithms for nonlinear optimization,” SIAM Review, vol. 28, no. 4, pp. 487–500, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. J. C. Gilbert and J. Nocedal, “Global convergence properties of conjugate gradient methods for optimization,” SIAM Journal on Optimization, vol. 2, no. 1, pp. 21–42, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. R. Pytlak, “On the convergence of conjugate gradient algorithms,” IMA Journal of Numerical Analysis, vol. 14, no. 3, pp. 443–460, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. G. Li, C. Tang, and Z. Wei, “New conjugacy condition and related new conjugate gradient methods for unconstrained optimization,” Journal of Computational and Applied Mathematics, vol. 202, no. 2, pp. 523–539, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. X. Li and X. Zhao, “A hybrid conjugate gradient method for optimization problems,” Natural Science, vol. 3, no. 1, pp. 85–90, 2011. View at Publisher · View at Google Scholar
  13. Y. H. Dai and Y. Yuan, “An efficient hybrid conjugate gradient method for unconstrained optimization,” Annals of Operations Research, vol. 103, pp. 33–47, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. W. W. Hager and H. Zhang, “A new conjugate gradient method with guaranteed descent and an efficient line search,” SIAM Journal on Optimization, vol. 16, no. 1, pp. 170–192, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. D.-H. Li, Y.-Y. Nie, J.-P. Zeng, and Q.-N. Li, “Conjugate gradient method for the linear complementarity problem with S-matrix,” Mathematical and Computer Modelling, vol. 48, no. 5-6, pp. 918–928, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  16. D.-H. Li and X.-L. Wang, “A modified Fletcher-Reeves-type derivative-free method for symmetric nonlinear equations,” Numerical Algebra, Control and Optimization, vol. 1, no. 1, pp. 71–82, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  17. L. Zhang, W. Zhou, and D. Li, “Global convergence of a modified Fletcher-Reeves conjugate gradient method with Armijo-type line search,” Numerische Mathematik, vol. 104, no. 4, pp. 561–572, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. L. Zhang, W. Zhou, and D.-H. Li, “A descent modified Polak-Ribière-Polyak conjugate gradient method and its global convergence,” IMA Journal of Numerical Analysis, vol. 26, no. 4, pp. 629–640, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. D. H. Li and X. J. Tong, Numerical Optimization, Science Press, Beijing, China, 2005.
  20. J. J. Moré, B. S. Garbow, and K. E. Hillstrom, “Testing unconstrained optimization software,” ACM Transactions on Mathematical Software, vol. 7, no. 1, pp. 17–41, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet