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A Modified Cut-Peak Function Method for Global Optimization

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Advances in Global Optimization

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 95))

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Abstract

We present a cut-peak function method for finding a global minimizer of the bound constrained optimization problems. A simple cut-peak function and choice function are defined at a local minimizer. By minimizing the choice function, a global descent of the original objective function is assured. Since the pattern search method does not require the gradient of the choice function, smoothing technique is not employed. The new algorithm is simple to implement and numerical results indicate its efficiency.

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References

  1. Ge, R.: A filled function method for finding a global minimizer of a function of several variables. Math. Prog. 46, 191–204 (1990)

    Article  MATH  Google Scholar 

  2. Liang, Y., Zhang, L., Li, M., Han, B.: A filled function method for global optimization. J. Comput. Appl. Math. 205, 16–31 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  3. Wu, Z., Zhang, L., Bai, F.: NewModified function method for global optimization. J. Optim. Theory Appli. 125, 181–203 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  4. Wu, Z., Zhang, L.: Global descent methods for unconstrained global optimization. J. Glob. Optim. 50, 379–396 (2011)

    Article  MATH  Google Scholar 

  5. Zhang, L., Fang, L.,Wang, Y.: A new tunnel function method for global optimization. Pac. J. Optim. 46, 125–138 (2008)

    MathSciNet  Google Scholar 

  6. Wang, Y., Fang, W., Wu, T.: A cut-peak function method for global optimization. J. Comput. Appl. Math. 230, 135–142 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  7. Huang, Z., Miao, X., Wang, P.: A revised cut-peak function method for box constrained continuous global optimization. Appl. Math. Comput. 194, 224–233 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  8. Sun, L., He, G., Wang, Y., Fang, L.: An active set quasi-Newton method with projected search for bound constrained minimization. Comput. Math. Appl. 58, 161–170 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  9. Sun, L., He, G.,Wang, Y., Zhou, C.: An accurate active set Newton method for large scale bound constrained optimization. Appl. Math. 56, 297–314 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  10. Sun, L., He, G., Zhou, C.: An active set strategy based on the multiplier function or the gradient. Appl. Math. 55, 291–304 (2010)

    Article  MATH  MathSciNet  Google Scholar 

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Acknowledgements

The work was supported in part by the National Science Foundation of China (10901094,11301307), the Excellent Young Scientist Foundation of Shangdong Province (BF2011SF024, BF2012SF025), and Young Teacher Foundation of Shandong Agricultural University (23744).

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Authors and Affiliations

  1. College of Information Science and Engineering, Shandong Agricultural University, Taian, 271018, China

    Sun Li & Wang Yuncheng

  2. Postdoctoral Station of Agricultural Resources and Environment, Shandong Agricultural University, Taian, 271018, China

    Sun Li & Wang Yuncheng

Authors
  1. Sun Li
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  2. Wang Yuncheng
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Corresponding author

Correspondence to Sun Li .

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Editors and Affiliations

  1. School of Science, Information Technology and Engineering, Federation University Australia, Ballarat, Victoria, Australia

    David Gao

  2. School Science, Inform., Tech. & Engg., Federation University Australia, Ballarat, Victoria, Australia

    Ning Ruan

  3. Dept. of Mathematical Sciences, Tsinghua University, Beijing, China

    Wenxun Xing

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Li, S., Yuncheng, W. (2015). A Modified Cut-Peak Function Method for Global Optimization. In: Gao, D., Ruan, N., Xing, W. (eds) Advances in Global Optimization. Springer Proceedings in Mathematics & Statistics, vol 95. Springer, Cham. https://doi.org/10.1007/978-3-319-08377-3_6

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