×

zbMATH — the first resource for mathematics

A new filled function for unconstrained global optimization. (English) Zbl 1120.90042
Summary: Seeking global optima of an unconstrained and multi-modal global optimization problem \(\min_{x\in \Omega}f(x)\) by constructing a filled function is concerned in this paper. On the basis of analyzing filled functions presented before, a new filled function is proposed, and it is proved to meet the properties of a filled function. Moreover, solutions of numerical experiments show that the function is quite effective.

MSC:
90C26 Nonconvex programming, global optimization
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Baba, N., Global optimization of functions by the random optimization method, International journal of control, 30, 1061-1065, (1979) · Zbl 0431.90058
[2] Basso, P., Iterative methods for the localization of the global maximum, SIAM journal on numerical analysis, 19, 781-792, (1982) · Zbl 0483.65038
[3] Branin, F., Widely convergent methods for finding multiple solutions of simultaneous nonlinear equations, IBM journal of research developments, 16, 504-522, (1972) · Zbl 0271.65034
[4] Dorea, C., Limiting distribution for random optimization methods, SIAM journal on control and optimization, 24, 76-82, (1986) · Zbl 0597.90070
[5] Ge, R.P., A filled function method for finding a global minimizer of a function of several variables, Mathematical programming, 46, 191-204, (1990) · Zbl 0694.90083
[6] Ge, R.P.; Qin, Y.F., A class of filled functions for finding global minimizers of a function of several variables, Journal of optimization theory and applications, 54, 241-252, (1987) · Zbl 0595.65072
[7] Kong, M.; Zhuang, J.-n., A class of new filled functions for pursuing the global minima of a non-smooth function with multi variables, Collegial transaction of computational mathematics, 18, 2, 165-174, (1996), (in Chinese)
[8] Levy, A.V.; Montalvo, A., The tunneling algorithm for the global minimization of functions, SIAM journal on scientific and statistical computing, 6, 15-29, (1985) · Zbl 0601.65050
[9] Li, B.-x.; Sheng, Y., Filled functions method for the Lipschitz programming, Systems mathematics and science, 11, 4, 346-348, (1991), (in Chinese)
[10] Liu, X., A class of generalized filled functions with improved computability, Journal of computational and applied mathematics, 137, 61-69, (2001) · Zbl 0990.65066
[11] Liu, X., Several filled functions with mitigators, Applied mathematics and computation, 133, 375-387, (2002) · Zbl 1135.90372
[12] Snyman, J.; Fatti, L., A multi-start global minimization algorithm with dynamic search trajectories, Journal of optimization theory and applications, 54, 121-141, (1987) · Zbl 0595.90073
[13] Törn, A., Cluster analysis using seed points and density determined hyperspheres as an aid to global optimization, IEEE transactions on systems, man, and cybernetics, 7, 610-616, (1977) · Zbl 0361.62053
[14] Wales, D.J.; Scheraga, H.A., Global optimization of clusters, crystals and biomolecules, Science, 285, 1368-1372, (1999)
[15] Xu, Z.; Huang, H.-x.; Pardalos, P.M.; Xu, C.-x., Filled functions for unconstrained global optimization, Journal of global optimization, 20, 49-65, (2001) · Zbl 1049.90092
[16] Zhang, L.-y.; Liu, S.-y.; Ge, Z.-h., A revised filled function for the global optimzation of the Lipschitz programming, Collegial transaction of computational mathematics, 25, 2, 153-159, (2003), (in Chinese)
[17] Zhang, L.-s.; Chi-kong, N.G.; Li, Duan; Tian, Wei-wen, A new filled function method for global optimization, Journal of global optimization, 28, 17-43, (2004) · Zbl 1061.90109
[18] Zhu, Wen-xing; Fu, Qing-xiang, A sequential convexification method (SCM) for continuous global optimization, Journal of global optimization, 26, 167-182, (2003) · Zbl 1049.90069
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.