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Modelling and Data Analysis
2020. Vol. 10, no. 1, 110–128
doi:10.17759/mda.2020100107
ISSN: 2219-3758 / 2311-9454 (online)

Algorithmization and Software Implementation of the Method of Eliminating Variables in Polynomial Optimization Problems

109

V.N. Nefedov, A.V. Zharkikh

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Abstract

The method of sequential exclusion of variables in polynomial optimization problems is considered. A number of problems are solved using this method. The practical steps of an algorithm are described, which reduces the initial polynomial optimization problem to a multi-stage branching process of obtaining a finite number of alternative problems, the output of which gives a finite set of polynomials in one variable. As a result, solving a number of polynomial problems reduces to sorting out a finite number of vectors whose components are the real roots of polynomials.

General Information

Keywords: polynomials, exclusion of variables, optimization problems, systems of algebraic equations

Journal rubric: Optimization Methods

Article type: scientific article

DOI: https://doi.org/10.17759/mda.2020100107

For citation: Nefedov V.N., Zharkikh A.V. Algorithmization and Software Implementation of the Method of Eliminating Variables in Polynomial Optimization Problems. Modelirovanie i analiz dannikh = Modelling and Data Analysis, 2020. Vol. 10, no. 1, pp. 110–128. DOI: 10.17759/mda.2020100107. (In Russ., аbstr. in Engl.)

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Information About the Authors

Viktor N. Nefedov, PhD in Physics and Matematics, Associate Professor, Department of Mathematical Cybernetics, Moscow Aviation Institute (MAI), Moscow, Russia, e-mail: nefedovvn54@yandex.ru

Aleksey V. Zharkikh, Master’s Degree Student at the Faculty of Information Technology and Applied Mathematics, Moscow Aviation Institute (MAI), Moscow, Russia, e-mail: alexvzhar@gmail.com

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