THE LOCALIZATION METHOD OF EXTREMUM POINT FOR UNIMODAL FUNCTION

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J. of Mech. Eng., 2016, vol. 19, no. 1, pp. 44-53

DOI:  https://doi.org/10.15407/pmach2016.01.044

Journal Journal of Mechanical Engineering
Publisher A. Podgorny Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
ISSN 0131-2928 (Print), 2411-0779 (Online)
Issue Vol. 19, no. 1, 2016 (March)
Pages 44–53

 

Authors

G. A. Sheludko, A. Podgorny Institute of Mechanical Engineering Problems of NASU (2/10, Pozharsky St., Kharkiv, 61046, Ukraine)

S. V. Ugrimov, A. Podgorny Institute of Mechanical Engineering Problems of NASU (2/10, Pozharsky St., Kharkiv, 61046, Ukraine), e-mail: sugrimov@ipmach.kharkov.ua, ORCID: 0000-0002-0846-4067

 

Abstract

Three-point methods of searching for the extremum of a piecewise non-smooth function are considered. Special attention is paid to the application of methods for solving problems with poor conditioning, which is caused by the divergence of the function being minimized. Owing to the combination of linear Regula falsi methods and secants, it has become possible to significantly increase the effectiveness of the search tool. The test examples demonstrate the effect of the proposed approach.

 

Keywords: extremum, unimodal function, one-dimensional search, piecewise linear approximation, weighted average operations, characteristic numbers, efficiency index

 

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Received 02 March 2016