On the convergence of the Baba and Dorea random optimization methods
type: Item
instance of: scholarly article
title: On the convergence of the Baba and Dorea random optimization methods
zbMATH Open document ID: 0683.90071
DOI: 10.1007/BF00939542
published in: Journal of Optimization Theory and Applications
publication date: 1990-01-01T00:00:00Z
review text: The global minimization methods of \textit{N. Baba} [ibid. 33, 451-461 (1981; Zbl 0453.90069)] and \textit{C. C. Y. Dorea} [ibid. 39, 165-171 (1983; Zbl 0479.93078)] 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 the 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.
Mathematics Subject Classification ID: 90C90
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90-08
zbMATH DE Number: 4119950
zbMATH Keywords: numerical convergence
zbMATH Keywords: global minimization
zbMATH Keywords: transformer design function
zbMATH Keywords: random optimization methods
Wikidata QID: Q56137800
author: M. S. Sarma
MaRDI profile type: Publication
cites work: Convergence of a random optimization method for constrained optimization problems
cites work: Expected number of steps of a random optimization method
cites work: An algorithm for the solution of constrained generalised polynomial programming problems
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description: scientific article; zbMATH DE number 4119950