Abstract
The Baba and Dorea global minimization methods have been applied to two physical problems. The first one is that of finding the global minimum of the transformer design function of six variables subject to constraints. The second one is the problem of fitting the orbit of a satellite using a set of observations. The latter problem is reduced to that of finding the global minimum of the sum of the squares of the differences between the observed values of the azimuth, elevation, and range at certain intervals of time from the epoch and the computed values of the azimuth, elevation, and range at the same intervals of time. Baba and Dorea established theoretically that the random optimization methods converge to the global minimum with probability one. The numerical experiments carried out for the above two problems show that convergence is very slow for the first problem and is even slower for the second problem. In both cases, it has not been possible to reach the global minimum if the search domains of the variables are wide, even after a very large number of function evaluations.
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References
Baba, N.,Convergence of a Random Optimization Method for Constrained Optimization Problems, Journal of Optimization Theory and Applications, Vol. 33, pp. 451–461, 1981.
Dorea, C. C. Y.,Expected Number of Steps of a Random Optimization Method, Journal of Optimization and Applications, Vol. 39, pp. 165–171, 1983.
Ballard, D. H., Jelinek, C. O., andSchinzinger, R.,An Algorithm for the Solution of Constrained Generalized Polynomial Programming Problems, Computer Journal, Vol. 17, pp. 261–266, 1974.
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Communicated by M. Avriel
The author thanks the referee for his suggestions on improving the presentation of the paper.
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Sarma, M.S. On the convergence of the Baba and Dorea random optimization methods. J Optim Theory Appl 66, 337–343 (1990). https://doi.org/10.1007/BF00939542
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DOI: https://doi.org/10.1007/BF00939542