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Year 2019, Volume: 2 Issue: 1, 34 - 42, 02.08.2019

Ahmet Sahıner İdris A. Masoud Abdulhamıd Shehab A. Ibrahem

Abstract

References

  • [1] Y. Lin and Y. Yang, Filled function method for nonlinear equations, Journal of Computational and Applied Mathematics, vol. 234, no. 3, pp. 695702, 2010.
  • [2] 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. 241252, 1987.
  • [3] 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. 191204, 1990.
  • [4] Y. Zhang, L. Zhang, and Y. Xu, New filled functions for nonsmooth global optimization, Applied Mathematical Modelling, vol. 33, no. 7, pp. 31143129, 2009.
  • [5] E. K. Chong, & S. H.Zak, An introduction to optimization. Vol. 76. John Wiley & Sons, 2013.
  • [6] W. Wang, Y. Shang, and L. Zhang, A filled function method with one parameter for box constrained global optimization, Applied Mathematics and Computation, vol. 194, no. 1, pp. 5466, 2007.
  • [7] X. Liu, Finding global minima with a computable filled function, Journal of Global Optimization, vol. 19, no. 2, pp. 151161, 2001.
  • [8] A. Sahiner, S. A. Ibrahem, A new global optimization technique by auxiliary function method in a directional search, Optim. Lett. 2018, doi: 10.1007/s11590-018-1315-1.

A new filled function method with two parameters in a directional search

Year 2019, Volume: 2 Issue: 1, 34 - 42, 02.08.2019

Ahmet Sahıner İdris A. Masoud Abdulhamıd Shehab A. Ibrahem

Abstract

In this paper, We consider the problem of finding the global minimizer point of a given multi-dimensional unconstrained objective function, for that a new algorithm developed, this algorithm based on two steps. First, we transform our problem into one-dimension according to the number of directions. Second, we construct a new filled function at each direction to minimize the one-dimension problem to reduce the number of local minimizers and then we find the global minimizer of the multi-dimensional objective function. We present the results of numerical experiments using test problems taken from literature studies. Numerical results obtained indicate the efficiency and reliability of the proposed filled function methods.

Keywords

global optimization filled function method

References

  • [1] Y. Lin and Y. Yang, Filled function method for nonlinear equations, Journal of Computational and Applied Mathematics, vol. 234, no. 3, pp. 695702, 2010.
  • [2] 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. 241252, 1987.
  • [3] 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. 191204, 1990.
  • [4] Y. Zhang, L. Zhang, and Y. Xu, New filled functions for nonsmooth global optimization, Applied Mathematical Modelling, vol. 33, no. 7, pp. 31143129, 2009.
  • [5] E. K. Chong, & S. H.Zak, An introduction to optimization. Vol. 76. John Wiley & Sons, 2013.
  • [6] W. Wang, Y. Shang, and L. Zhang, A filled function method with one parameter for box constrained global optimization, Applied Mathematics and Computation, vol. 194, no. 1, pp. 5466, 2007.
  • [7] X. Liu, Finding global minima with a computable filled function, Journal of Global Optimization, vol. 19, no. 2, pp. 151161, 2001.
  • [8] A. Sahiner, S. A. Ibrahem, A new global optimization technique by auxiliary function method in a directional search, Optim. Lett. 2018, doi: 10.1007/s11590-018-1315-1.
There are 8 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Ahmet Sahıner 0000-0002-4945-2476

İdris A. Masoud Abdulhamıd This is me 0000-0002-6272-8318

Shehab A. Ibrahem 0000-0003-2428-2703

Publication Date August 2, 2019
Published in Issue Year 2019 Volume: 2 Issue: 1

Cite

APA Sahıner, A., Abdulhamıd, İ. A. M., & Ibrahem, S. A. (2019). A new filled function method with two parameters in a directional search. Journal of Multidisciplinary Modeling and Optimization, 2(1), 34-42.
AMA Sahıner A, Abdulhamıd İAM, Ibrahem SA. A new filled function method with two parameters in a directional search. jmmo. August 2019;2(1):34-42.
Chicago Sahıner, Ahmet, İdris A. Masoud Abdulhamıd, and Shehab A. Ibrahem. “A New Filled Function Method With Two Parameters in a Directional Search”. Journal of Multidisciplinary Modeling and Optimization 2, no. 1 (August 2019): 34-42.
EndNote Sahıner A, Abdulhamıd İAM, Ibrahem SA (August 1, 2019) A new filled function method with two parameters in a directional search. Journal of Multidisciplinary Modeling and Optimization 2 1 34–42.
IEEE A. Sahıner, İ. A. M. Abdulhamıd, and S. A. Ibrahem, “A new filled function method with two parameters in a directional search”, jmmo, vol. 2, no. 1, pp. 34–42, 2019.
ISNAD Sahıner, Ahmet et al. “A New Filled Function Method With Two Parameters in a Directional Search”. Journal of Multidisciplinary Modeling and Optimization 2/1 (August 2019), 34-42.
JAMA Sahıner A, Abdulhamıd İAM, Ibrahem SA. A new filled function method with two parameters in a directional search. jmmo. 2019;2:34–42.
MLA Sahıner, Ahmet et al. “A New Filled Function Method With Two Parameters in a Directional Search”. Journal of Multidisciplinary Modeling and Optimization, vol. 2, no. 1, 2019, pp. 34-42.
Vancouver Sahıner A, Abdulhamıd İAM, Ibrahem SA. A new filled function method with two parameters in a directional search. jmmo. 2019;2(1):34-42.
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