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

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

Kaynakça

1. [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. [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. [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. [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. [5] E. K. Chong, & S. H.Zak, An introduction to optimization. Vol. 76. John Wiley & Sons, 2013.
6. [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. [7] X. Liu, Finding global minima with a computable filled function, Journal of Global Optimization, vol. 19, no. 2, pp. 151161, 2001.
8. [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.