Article Outline
Keywords and Phrases
Introduction
Definitions
Methods
Two-Parameter Filled Functions
Single-Parameter Filled Functions
Nonsmooth Filled Functions
Discrete Filled Functions
Summary
References
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Dixon LCW, Gomulka J, Hersom SE (1976) Reflections on global optimization. In: Dixon LCW Optimization in Action. Academic Press, New York, pp 398–435
Fletcher R (1981) Practical Methods of Optimization, vol 2. Wiley, New York
Ge RP (1987) The theory of filled function methods for finding global minimizers of nonlinearly constrained minimization problems. Presented at SIAM Conference on Numerical Optimization, Boulder, Colorado, 1984. See also J Comput Math 5(1):1–9
Ge RP (1989) A parallel global optimization algorithm for rational separable-fractorable functions. Appl Math Comput 32(1):61–72
Ge RP (1990) A filled function method for finding a global minimizer of a function of several variables. Presented at the Dundee Conference on Numerical Analysis, Dunded, Scotland, 1983. See also Math Programm 46:191–204
Ge RP, Huang CB (1989) A continuous approach to nonlinear integer programming. Appl Math Comput 34(1):39–60
Ge RP, Qin YF (1987) A class of filled functions for finding global minimizers of a function of several variables. J Optim Theory Appl 54(2):241–252
Ge RP, Qin YF (1990) The globally convexized filled functions for globally optimization. Appl Math Comput 35:131–158
Huang HX, Zhao Y (2007) A hybrid global optimization algorithm based on locally filled functions and cluster analysis. Int J Comput Sci Eng 3:194–202
Kong M, Zhuang JN (1996) A modified filled function method for finding a global minimizer of a non-smooth function of several variables (In Chinese). Num Math J Chinese Univ 18(2):165–174
Liu X (2001) Finding global minima with a computable filled function. J Global Optim 19:151–161
Liu X (2002) A computable filled function used for global minimization. Appl Math Comput 126(2–3):271–278
Liu X (2002) Several filled functions with mitigators. Appl Math Comput 133(2–3):375–387
Liu X (2004) Two new classes of filled functions. Appl Math Comput 149(2):577–588
Liu X (2004) The impelling function method applied to global optimization. Appl Math Comput 151(3):745–754
Lucidi S, Piccialli V (2002) New classes of global convexized filled functions for global optimization. J Global Optim 24:219–236
Ng CK, Zhang LS, Li D, Tian WW (2005) Discrete filled function method for discrete global optimization. Comput Optim Appl 31:87–115
Wu ZY, Li HWJ, Zhang LS, Yang XM (2006) A novel filled function method and quasi-filled function method for global optimization. Comput Optim Appl 34(2):249–272
Wu ZY, Zhang LS, Teo KL, Bai FS (2005) New modified function method for global optimization. J Optim Theory Appl 125(1):181–203
Xu Z, Huang HX, Pardalos PM, Xu CX (2001) Filled functions for unconstrained global optimization. J Global Optim 20:49–65
Zhang LS, Ng CK, Li D, Tian WW (2004) A new filled function method for global optimization. J Global Optim 28:17–43
Zhao Y (2006) Study of hybrid optimization methods based on locally filled functions. Master Thesis (In Chinese), Tsinghua University
Zhu WX (1998) An approximate algorithm for nonlinear integer programming. Appl Math Comput 93(2/3):183–193
Zhuang JN (1994) A generalized filled function method for finding the global minimizer of a function of several variables (In Chinese). Num Math J Chinese Univ 16(3):279–287
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© 2008 Springer-Verlag
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Huang, HX. (2008). Global Optimization: Filled Function Methods . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_231
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DOI: https://doi.org/10.1007/978-0-387-74759-0_231
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-74758-3
Online ISBN: 978-0-387-74759-0
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