Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 843609, 10 pages
doi:10.1155/2010/843609
Research Article

Finding Global Minima with a Filled Function Approach for Non-Smooth Global Optimization

Weixiang Wang,1 Youlin Shang,2 and Ying Zhang3

1Department of Mathematics, Shanghai Second Polytechnic University, Shanghai 201209, China
2Department of Mathematics, Henan University of Science and Technology, Luoyang 471003, China
3Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China

Received 12 October 2009; Accepted 5 February 2010

Academic Editor: Elena Braverman

Copyright © 2010 Weixiang Wang 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. R. P. Ge, “A filled function method for finding a global minimizer of a function of several variables,” Mathematical Programming, vol. 46, no. 2, pp. 191–204, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. P. M. Pardalos, H. E. Romeijn, and H. Tuy, “Recent developments and trends in global optimization,” Journal of Computational and Applied Mathematics, vol. 124, no. 1-2, pp. 209–228, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. P. M. Pardalos and H. E. Romeijn, Eds., Handbook of Global Optimization. Vol. 22: Heuristic Approaches, vol. 62 of Nonconvex Optimization and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2002. View at MathSciNet
  4. R. Horst and P. M. Pardalos, Eds., Handbook of Global Optimization, vol. 2 of Nonconvex Optimization and Its Applications, Kluwer Academic Publishers, Dordrecht, Netherlands, 1995. View at MathSciNet
  5. Z. Xu, H.-X. Huang, P. M. Pardalos, and C.-X. Xu, “Filled functions for unconstrained global optimization,” Journal of Global Optimization, vol. 20, no. 1, pp. 49–65, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. Y. Yang and Y. Shang, “A new filled function method for unconstrained global optimization,” Applied Mathematics and Computation, vol. 173, no. 1, pp. 501–512, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. X. Wang and G. Zhou, “A new filled function for unconstrained global optimization,” Applied Mathematics and Computation, vol. 174, no. 1, pp. 419–429, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. L.-S. Zhang, C.-K. Ng, D. Li, and W.-W. Tian, “A new filled function method for global optimization,” Journal of Global Optimization, vol. 28, no. 1, pp. 17–43, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. Q. Wu, S. Y. Liu, L. Y. Zhang, and C. C. Liu, “A modified filled function method for global minimization of a nonsmooth programming problem,” Mathematica Applicata, vol. 17, no. 2, pp. 36–40, 2004. View at MathSciNet
  10. L. S. Zhang, “On the solving global optimization approach from local to global,” Journal of Chongqing, vol. 26, no. 1, pp. 1–6, 2009.
  11. H. F. Clark, Optimization and Non-Smooth Analysis, SIAM, Philadelphia, Pa, USA, 1990.
  12. C. J. Price, B. L. Robertson, and M. Reale, “A hybrid Hooke and Jeeves—direct method for non-smooth optimization,” Advanced Modeling and Optimization, vol. 11, no. 1, pp. 43–61, 2009. View at Zentralblatt MATH · View at MathSciNet
  13. C. Audet and J. E. Dennis Jr., “Mesh adaptive direct search algorithms for constrained optimization,” SIAM Journal on Optimization, vol. 17, no. 1, pp. 188–217, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet