Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2015, Article ID 352524, 8 pages
http://dx.doi.org/10.1155/2015/352524
Research Article

A New Conjugate Gradient Algorithm with Sufficient Descent Property for Unconstrained Optimization

1School of Economic Management, Xi’an University of Posts and Telecommunications, Shaanxi, Xi’an 710061, China
2School of Mathematics Science, Liaocheng University, Shandong, Liaocheng 252000, China

Received 16 May 2015; Revised 24 September 2015; Accepted 29 September 2015

Academic Editor: Masoud Hajarian

Copyright © 2015 XiaoPing Wu et al. 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. G. Zoutendijk, “Nonlinear programming computational methods,” in Integer and Non-Linear Programming, J. Abadie, Ed., pp. 37–86, North-Holland Publishing, Amsterdam, The Nertherlands, 1970. View at Google Scholar
  2. M. Al-Baali, “Descent property and global convergence of the fletcher-reeves method with inexact line search,” IMA Journal of Numerical Analysis, vol. 5, no. 1, pp. 121–124, 1985. View at Publisher · View at Google Scholar · View at Scopus
  3. Y. H. Dai and Y. Yuan, “An efficient hybrid conjugate gradient method for unconstrained optimization,” Annals of Operations Research, vol. 103, no. 1–4, pp. 33–47, 2001. View at Publisher · View at Google Scholar · View at Scopus
  4. Z. X. Wei, G. Y. Li, and L. Q. Qi, “Global convergence of the Polak-Ribière-Polyak conjugate gradient method with an Armijo-type inexact line search for nonconvex unconstrained optimization problems,” Mathematics of Computation, vol. 77, no. 264, pp. 2173–2193, 2008. View at Publisher · View at Google Scholar · View at Scopus
  5. 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, 2000. View at Google Scholar · View at Scopus
  6. S. W. Yao, Z. X. Wei, and H. Huang, “A note about WYL's conjugate gradient method and its applications,” Applied Mathematics and Computation, vol. 191, no. 2, pp. 381–388, 2007. View at Publisher · View at Google Scholar
  7. X. Z. Jiang, G. D. Ma, and J. B. Jian, “A new global convergent conjugate gradient method with Wolfe line search,” Chinese Journal of Engineering Mathematics, vol. 28, no. 6, pp. 779–786, 2011. View at Google Scholar · View at MathSciNet
  8. X. Z. Jiang, L. Han, and J. B. Jian, “A globally convergent mixed conjugate gradient method with Wolfe line search,” Mathematica Numerica Sinica, vol. 34, no. 1, pp. 103–112, 2012. View at Google Scholar · View at MathSciNet
  9. D. Touati-Ahmed and C. Storey, “Efficient hybrid conjugate gradient techniques,” Journal of Optimization Theory and Applications, vol. 64, no. 2, pp. 379–397, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  10. 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
  11. Y. F. Hu and C. Storey, “Global convergence result for conjugate gradient methods,” Journal of Optimization Theory and Applications, vol. 71, no. 2, pp. 399–405, 1991. View at Publisher · View at Google Scholar
  12. L. Grippo and S. Lucidi, “A globally convergent version of the polak-ribière conjugate gradient method,” Mathematical Programming, Series B, vol. 78, no. 3, pp. 375–391, 1997. View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  13. G. H. Yu, L. T. Guan, and G. Y. Li, “Global convergence of modified Polak-Ribière-Polyak conjugate gradient methods with sufficient descent property,” Journal of Industrial and Management Optimization, vol. 4, no. 3, pp. 565–579, 2008. View at Publisher · View at Google Scholar · View at Scopus
  14. N. Andrei, “Numerical comparison of conjugate gradient algorithms for unconstrained optimization,” Studies in Informatics & Control, vol. 16, no. 4, pp. 333–352, 2007. View at Google Scholar
  15. Y. H. Dai, Analyses of conjugate gradient methods [Ph.D. thesis], Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, 1997.
  16. G. Yu, L. Guan, and G. Li, “Global convergence of modified Polak-Ribière-Polyak conjugate gradient methods with sufficient descent property,” Journal of Industrial and Management Optimization, vol. 4, no. 3, pp. 565–579, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  17. Y.-H. Dai and C.-X. Kou, “A nonlinear conjugate gradient algorithm with an optimal property and an improved wolfe line search,” SIAM Journal on Optimization, vol. 23, no. 1, pp. 296–320, 2013. View at Publisher · View at Google Scholar · View at Scopus
  18. X.-Z. Jiang and J.-B. Jian, “Two modified nonlinear conjugate gradient methods with disturbance factors for unconstrained optimization,” Nonlinear Dynamics, vol. 77, no. 1-2, pp. 387–397, 2014. View at Publisher · View at Google Scholar · View at Scopus
  19. J. B. Jian, L. Han, and X. Z. Jiang, “A hybrid conjugate gradient method with descent property for unconstrained optimization,” Applied Mathematical Modelling, vol. 39, pp. 1281–1290, 2015. View at Google Scholar
  20. Z. Wei, G. Li, and L. Qi, “New nonlinear conjugate gradient formulas for large-scale unconstrained optimization problems,” Applied Mathematics and Computation, vol. 179, no. 2, pp. 407–430, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  21. H. Huang, Z. Wei, and Y. Shengwei, “The proof of the sufficient descent condition of the Wei-Yao-Liu conjugate gradient method under the strong Wolfe-Powell line search,” Applied Mathematics and Computation, vol. 189, no. 2, pp. 1241–1245, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  22. G. Yu, Y. Zhao, and Z. Wei, “A descent nonlinear conjugate gradient method for large-scale unconstrained optimization,” Applied Mathematics and Computation, vol. 187, no. 2, pp. 636–643, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  23. P. Wolfe, “Convergence conditions for ascent methods,” SIAM Review, vol. 11, no. 2, pp. 226–235, 1969. View at Publisher · View at Google Scholar · View at Scopus
  24. P. Wolfe, “Convergence conditions for ascent methods. ii: some corrections,” SIAM Review, vol. 13, no. 2, pp. 185–188, 1971. View at Publisher · View at Google Scholar
  25. Y. Dai and Y. Yuan, Nonlinear Conjugate Methods, Science Press of Shanghai, Shanghai, China, 2000.
  26. I. Bongartz, A. R. Conn, N. Gould, and P. L. Toint, “CUTE: constrained and unconstrained testing environment,” ACM Transactions on Mathematical Software, vol. 21, no. 1, pp. 123–160, 1995. View at Publisher · View at Google Scholar · View at Scopus
  27. 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
  28. E. D. Dolan and J. J. Moré, “Benchmarking optimization software with performance profiles,” Mathematical Programming, Series B, vol. 91, no. 2, pp. 201–213, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus