×

Simple transformation functions for finding better minima. (English) Zbl 1144.90492

Summary: This work presents two transformation functions, the \(\alpha\)-function and the \(M\)-function, for finding better minimizers in global optimization. We prove that under some general assumptions these functions possess the characters of both tunnelling functions and filled functions. Numerical tests from some test functions show that our transformation functions are very effective in finding better minima.

MSC:

90C30 Nonlinear programming
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] (Dixon, L. C.W.; Szegö, G. P., Towards Global Optimization (1975), North-Holland: North-Holland Amsterdam) · Zbl 0309.90052
[2] Ge, R. P.; Qin, Y. F., A class of filled functions for finding a global minimizer of a function of several variables, J. Optim. Theory Appl., 54, 2, 241-252 (1987) · Zbl 0595.65072
[3] Ge, R. P., A filled function method for finding a global minimizer of a function of several variables, Math. Program., 46, 191-204 (1990) · Zbl 0694.90083
[4] Ge, R. P.; Qin, Y. F., The globally convexized filled functions for global optimization, Appl. Math. Comput., 35, 131-158 (1990) · Zbl 0752.65052
[5] Han, Q. M.; Han, J. Y., Revised filled function methods for global optimization, Appl. Math. Comput., 119, 217-228 (2001) · Zbl 1053.90111
[6] Horst, R.; Pardalos, P. M.; Thoai, N. V., Introduction to Global Optimization (1995), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht, Netherlands · Zbl 0836.90134
[7] Levy, A. V.; Montalvo, A., The tunneling algorithm for the global minimization of functions, SIAM J. Sci. Statist. Comput., 6, 1, 15-29 (1985) · Zbl 0601.65050
[8] Liu, X., Finding global minima with a computable filled function, J. Global Optim., 19, 151-161 (2001) · Zbl 1033.90088
[9] Lucidi, S.; Piccialli, V., New classes of globally convexized filled functions for global optimization, J. Global Optim., 24, 219-236 (2002) · Zbl 1047.90051
[10] Yao, Y., Dynamic tunneling algorithm for global optimization, IEEE Trans. Syst. Man Cybern., 19, 5, 1222-1230 (1989)
[11] Zhang, L. S.; Ng, C. K.; Li, D.; Tian, W. W., A new filled function method for global optimization, J. Global Optim., 28, 17-43 (2004) · Zbl 1061.90109
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.