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Journal of Applied Mathematics
Volume 2015 (2015), Article ID 245427, 8 pages
http://dx.doi.org/10.1155/2015/245427
Research Article

A Filled Function Method Dominated by Filter for Nonlinearly Global Optimization

1Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China
2Shangnan Middle School, South Campus, Shanghai 200123, China

Received 18 August 2014; Revised 30 December 2014; Accepted 8 January 2015

Academic Editor: George Fikioris

Copyright © 2015 Wei 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 and Y. F. Qin, “A class of filled functions for finding global minimizers of a function of several variables,” Journal of Optimization Theory and Applications, vol. 54, no. 2, pp. 241–252, 1987. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. R. P. Ge and Y. F. Qin, “The globally convexized filled functions for global optimization,” Applied Mathematics and Computation, vol. 35, no. 2, pp. 131–158, 1990. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. 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 MathSciNet · View at Scopus
  4. W. Wang and Y. Xu, “Simple transformation functions for finding better minima,” Applied Mathematics Letters, vol. 21, no. 5, pp. 502–509, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. Y. M. Liang, L. S. Zhang, M. M. Li, and B. S. Han, “A filled function method for global optimization,” Journal of Computational and Applied Mathematics, vol. 205, no. 1, pp. 16–31, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. H. Lin, Y. Wang, L. Fan, and Y. Gao, “A new discrete filled function method for finding global minimizer of the integer programming,” Applied Mathematics and Computation, vol. 219, no. 9, pp. 4371–4378, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. B. W. Ling, C. Z. Wu, K. L. Teo, and V. Rehbock, “Global optimal design of IIR filters via constraint transcription and filled function methods,” Circuits, Systems, and Signal Processing, vol. 32, no. 3, pp. 1313–1334, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. R. Fletcher and S. Leyffer, “Nonlinear programming without a penalty function,” Mathematical Programming, vol. 91, no. 2, pp. 239–269, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. R. Fletcher, S. Leyffer, and P. L. Toint, “On the global convergence of a filter-SQP algorithm,” SIAM Journal on Optimization, vol. 13, no. 1, pp. 44–59, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. A. Wachter and L. T. Biegler, “Line search filter methods for nonlinear programming: local convergence,” SIAM Journal on Optimization, vol. 16, no. 1, pp. 32–48, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. W. Wang, S. Hua, and J. Tang, “A generalized gradient projection filter algorithm for inequality constrained optimization,” Journal of Applied Mathematics, vol. 2013, Article ID 854890, 6 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  12. C. J. Wang, R. H. Luo, K. Wu, and B. S. Han, “A new filled function method for an unconstrained nonlinear equation,” Journal of Computational and Applied Mathematics, vol. 235, no. 6, pp. 1689–1699, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. Z. Y. Wu, F. S. Bai, G. Q. Li, and Y. J. Yang, “A new auxiliary function method for systems of nonlinear equations,” Journal of Industrial and Management Optimization, vol. 11, no. 2, pp. 345–364, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  14. C. A. Floudas, P. M. Pardalos, C. S. Adjiman et al., Handbook of Test Problems in Local and Global Optimization, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1999. View at Publisher · View at Google Scholar · View at MathSciNet