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A parallel method for finding the global minimum of univariate functions

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Abstract

We describe a new parallel method for solving global optimization problems. The formulation of the decision rules of this method is presented. We examine convergence conditions of the proposed algorithm and establish conditions which guarantee a considerable speedup with respect to the sequential version of the algorithm. We also present some numerical experiments executed on Alliant FX/80 for one class of multiextremal functions.

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Authors and Affiliations

  1. Nizhni Novgorod State University, Nizhni Novgorod, Russia

    Ya. D. Sergeyev (Associate Professor of Mathematics) & V. A. Grishagin

Authors
  1. Ya. D. Sergeyev
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  2. V. A. Grishagin
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Additional information

Communicated by G. Di Pillo

The authors are greatly indebted to R. G. Strongin who stimulated the fulfillment of this research. They also would like to thank the anonymous referees for their useful suggestions.

The research of the first author was partially supported by Grant 9494/NC/89 from the Italian Government under the Italian-Soviet Agreement about the Cultural and Scientific Exchange in 1990–1991. He thanks the Systems Department, University of Calabria, where he was a Visitor.

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Sergeyev, Y.D., Grishagin, V.A. A parallel method for finding the global minimum of univariate functions. J Optim Theory Appl 80, 513–536 (1994). https://doi.org/10.1007/BF02207778

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