On convergence rate of a rectangular partition based global optimization algorithm |
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Authors: | James Calvin Gražina Gimbutienė William O. Phillips Antanas Žilinskas |
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Affiliation: | 1.Department of Computer Science,New Jersey Institute of Technology,Newark,USA;2.Institute of Mathematics and Informatics,Vilnius University,Vilnius,Lithuania |
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Abstract: | The convergence rate of a rectangular partition based algorithm is considered. A hyper-rectangle for the subdivision is selected at each step according to a criterion rooted in the statistical models based theory of global optimization; only the objective function values are used to compute the criterion of selection. The convergence rate is analyzed assuming that the objective functions are twice- continuously differentiable and defined on the unit cube in d-dimensional Euclidean space. An asymptotic bound on the convergence rate is established. The results of numerical experiments are included. |
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