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A bridging method for global optimization

Published online by Cambridge University Press:  17 February 2009

Y. Liu  and
K. L. Teo
Y. Liu
Affiliation:
School of Mathematics and Statistics, Curtin University of Technology, Perth, WA 6001, Australia.
K. L. Teo
Affiliation:
School of Mathematics and Statistics, Curtin University of Technology, Perth, WA 6001, Australia.
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Abstract

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In this paper a bridging method is introduced for numerical solutions of one-dimensional global optimization problems where a continuously differentiable function is to be minimized over a finite interval which can be given either explicitly or by constraints involving continuously differentiable functions. The concept of a bridged function is introduced. Some properties of the bridged function are given. On this basis, several bridging algorithm are developed for the computation of global optimal solutions. The algorithms are demonstrated by solving several numerical examples.

Type
Research Article
Information
The ANZIAM Journal , Volume 41 , Issue 1 , July 1999 , pp. 41 - 57
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Bromberg, M. and Chang, T-S., “One dimensional optimization using linear lower bounds”, in Recent Advances in Global Optimization (eds Floudas, C. A. and Pardalos, P. M.), (Princeton University Press, 1992) 200–220.Google Scholar
[2]Floudas, C. A. and Pardalos, P. M. (eds), State of the art in Global Optimization (Kluwer Academic Publishers, Dordrecht, 1996).CrossRefGoogle Scholar
[3]Ge, R., “A filled function method for finding a global minimizer of a function of several variables”, Math. Programming 46 (1990) 191–204.Google Scholar
[4]Horst, R., Pardalos, P. M. and Thoai, N. V., Introduction to Global Optimization (Kluwer Academic Publishers, Dordrecht, 1995).Google Scholar
[5]Jennings, L. S. and Teo, K. L., “A computational algorithm for functional inequality constrained optimization problems”, Automatica 26 (1990) 371–375.CrossRefGoogle Scholar
[6]Minoux, M., Mathematical Programming, Theory and Applications (John Wiley and Sons, Chichester, 1986).Google Scholar
[7]Wang, X. and Chang, T.-S., “An improved univariate global optimization algorithm with improved linear lower bounding functions”, J. Global Optimization 8 (1996) 393–411.CrossRefGoogle Scholar
[8]Wang, X. and Chang, T-S., “A multivariate global optimization using linear bounding functions”, 1997, preprint.Google Scholar