×

zbMATH — the first resource for mathematics

A novel filled function method and quasi-filled function method for global optimization. (English) Zbl 1121.90105
Summary: This paper gives a new definition of a filled function, which eliminates certain drawbacks of the traditional definitions. Moreover, this paper proposes a quasi-filled function to improve the efficiency of numerical computation and overcomes some drawbacks of filled functions. Then, a new filled function method and a quasi-filled function method are presented for solving a class of global optimization problems. The global optimization approaches proposed in this paper will find a global minimum of original problem by implementing a local search scheme to the proposed filled function or quasi-filled function. Illustrative examples are provided to demonstrate the efficiency and reliability of the proposed scheme.

MSC:
90C26 Nonconvex programming, global optimization
90C30 Nonlinear programming
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] F.H. Branin, ”Widely convergent methods for finding multiple solutions of simultaneous nonlinear equations,” IBM Journal of Research Development, vol. 16, pp. 504–522, 1972. · Zbl 0271.65034
[2] L.C.M. Dixon and G.P. Szegö (Eds.), Towards Global Optimization 2, North-Holland: Amsterdam, 1978. · Zbl 0385.00011
[3] R. Ge, ”A filled function method for finding a global minimizer of a function of several variables,” Mathamatical Programming, vol. 46, pp. 191–204, 1990. · Zbl 0694.90083
[4] R. Ge, ”The globally convexized filled functions for global optimization,” Applied Mathematics and Computation, vol. 35, pp. 131–158, 1990. · Zbl 0752.65052
[5] C. Kanzow, ”Global optimization techniques for mixed complementarity problems,” Journal of Global Optimization, vol. 16, pp. 1–21, 2000. · Zbl 1009.90119
[6] X. Liu, ”Finding global minimia with a computable filled function,” Journal of Global Optimization, vol. 19, pp. 151–161, 2001. · Zbl 1033.90088
[7] X. Liu, ”Several filled functions with mitigators,” Applied Mathematics and Computation, vol. 133, pp. 375–387, 2002. · Zbl 1135.90372
[8] X. Liu, ”A class of genaralilized filled functions with improved computability,” Journal of Computational and Applied Mathematics, vol. 137, pp. 62–69, 2001. · Zbl 0990.65066
[9] S. Lucidi and V. Piccialli, ”New classes of global convexized filled functions for global optimization,” Journal of Global Optimization, vol. 24, pp. 219–236, 2002. · Zbl 1047.90051
[10] P.M. Pardalos, H.E. Romeijin and T. Hoang, ”Recent developments and trends in global optimization,” Journal of Computational and Applied Mathematics, vol. 124, pp. 209–228, 2000. · Zbl 0969.90067
[11] L. Rastrigin, ”Systems of Extremal Control,” Nauka, Moscow, 1974. · Zbl 0284.49002
[12] Z.Y. Wu, L.S. Zhang, K.L. Teo, F.S. Bai, ”A new modified function method for global optimization,” Journal of Optimization Theory and Applications, vol. 125, pp.181–203, 2005. · Zbl 1114.90100
[13] Z. Xu, H.X. Huang, P.M. Pardalos, ”Filled functions for unconstrained global optimization,” Journal of Global Optimization, vol. 20, pp. 49–65, 2001. · Zbl 1049.90092
[14] L.S. Zhang, C.K. NG, D. Li and W.W. Tian, ”A new filled function method for global optimization,” Journal of Global Optimization, vol. 28, pp. 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.