Journal of Applied Mathematics

A Filled Function Method Dominated by Filter for Nonlinearly Global Optimization

Wei Wang, Xiaoshan Zhang, and Min Li

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Abstract

This work presents a filled function method based on the filter technique for global optimization. Filled function method is one of the effective methods for nonlinear global optimization, since it can effectively find a better minimizer. Filter technique is applied to local optimization methods for its excellent numerical results. In order to optimize the filled function method, the filter method is employed for global optimizations in this method. A new filled function is proposed first, and then the algorithm and its properties are proved. The numerical results are listed at the end.

Article information

Source
J. Appl. Math., Volume 2015 (2015), Article ID 245427, 8 pages.

Dates
First available in Project Euclid: 15 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.jam/1429105029

Digital Object Identifier
doi:10.1155/2015/245427

Mathematical Reviews number (MathSciNet)
MR3310449

Zentralblatt MATH identifier
07000919

Citation

Wang, Wei; Zhang, Xiaoshan; Li, Min. A Filled Function Method Dominated by Filter for Nonlinearly Global Optimization. J. Appl. Math. 2015 (2015), Article ID 245427, 8 pages. doi:10.1155/2015/245427. https://projecteuclid.org/euclid.jam/1429105029


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References

  • 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.
  • 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.
  • 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.
  • W. Wang and Y. Xu, “Simple transformation functions for finding better minima,” Applied Mathematics Letters, vol. 21, no. 5, pp. 502–509, 2008.
  • 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.
  • 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.
  • 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.
  • R. Fletcher and S. Leyffer, “Nonlinear programming without a penalty function,” Mathematical Programming, vol. 91, no. 2, pp. 239–269, 2002.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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. \endinput