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A parameter-free filled function for unconstrained global optimization. (English) Zbl 1068.90098
Summary: The filled function method is an approach for finding a global minimum of multi-dimensional functions. With more and more relevant research, it becomes a promising way used in unconstrained global optimization. Some filled functions with one or two parameters have already been suggested. However, there is no certain criterion to choose a parameter appropriately. In this paper, a parameter-free filled function is proposed. The definition of the original filled function and assumptions of the objective function given by Ge are improved according to the presented parameter-free filled function. The algorithm and numerical results of test functions are reported. Conclusions are drawn in the end.

MSC:
90C30 Nonlinear programming
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[1] Ge R P. A filled function method for finding a global minimizer of a function of several variables[J]. Mathematical Programming, 1990,46:191–204. · Zbl 0694.90083 · doi:10.1007/BF01585737
[2] Ge R P, Qin Y F. A class of filled functions for finding global minimizers of a function of several variables[J]. Journal of Optimization Theory and Applications, 1987, 54(2):241–252. · Zbl 0595.65072 · doi:10.1007/BF00939433
[3] Xu Zheng, Huang Hong-xuan, Pardalos P. M, Xu Cheng-xian. Filled functions for unconstrained global optimization[J]. Journal of Global Optimization, 2001,20:49–65. · Zbl 1049.90092 · doi:10.1023/A:1011207512894
[4] Han Q M, Han J Y. Revised filled function methods for global optimization[J]. Applied Mathematics and Computation, 2001, 119:217–228. · Zbl 1053.90111 · doi:10.1016/S0096-3003(99)00266-0
[5] Liu Xian. Finding global minima with a computable filled function[J]. Journal of Global Optimization, 2000, 19:151–161. · Zbl 1033.90088 · doi:10.1023/A:1008330632677
[6] Horst R, Pardalos M P, Thoai N V. Introduction to Global Optimization[M]. Kluwer Academic Publishers, Dordrecht, Netherlands, 1995. · Zbl 0836.90134
[7] Bazaraa M S, Sherali H D, Shetty C M. Nonlinear Programming[M]. 2nd Edition, John Wiley & Sons, New York,1993.
[8] Zheng Q, Zhuang D. Integral global minimization: algorithms, implementations and numerical tests[J]. Journal of Global Optimization, 1995, 7(4):421–454. · Zbl 0846.90105 · doi:10.1007/BF01099651
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