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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2016, Volume 20, Number 4, Pages 755–768 (Mi vsgtu1500)  

Mathematical Modeling, Numerical Methods and Software Complexes

Method of searching for global extremum of a continuous function on a simplex

M. Yu. Livshits, A. P. Sizikov*

Samara State Technical University, Samara, 443100, Russian Federation

Abstract: A non-convex problem of mathematical programming is considered, which permissible region is a simplex. A two-stage algorithm is proposed for approximate solution of the problem. The region of global optimum is determined using the $\Psi$-transform method at the first stage; local “fine-tuning” of the solution is performed at the second stage. The $\Psi$-transform was modified taking into account the special features of the problem under consideration. $\Psi$-function is determined according to the results of statistical tests implemented using the generator of random points uniformly distributed over the simplex. The proposed method of reflection of regular simplexes is used for fine-tuning of the solution. An example of application of the developed algorithm for solving the problem of optimization of component composition of the hydrocarbon mixture is presented.

Keywords: optimization, non-convex problems, $\Psi$- transform method, uniform distribution over the simplex, multi-component mixtures.
* Author to whom correspondence should be addressed

DOI: https://doi.org/10.14498/vsgtu1500

Full text: PDF file (877 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 519.853.4
MSC: 90C26, 90-08
Original article submitted 12/VII/2016
revision submitted – 23/X/2016

Citation: M. Yu. Livshits, A. P. Sizikov, “Method of searching for global extremum of a continuous function on a simplex”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 20:4 (2016), 755–768

Citation in format AMSBIB
\Bibitem{LivSiz16}
\by M.~Yu.~Livshits, A.~P.~Sizikov
\paper Method of searching for global extremum of a continuous function on a simplex
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2016
\vol 20
\issue 4
\pages 755--768
\mathnet{http://mi.mathnet.ru/vsgtu1500}
\crossref{https://doi.org/10.14498/vsgtu1500}
\zmath{https://zbmath.org/?q=an:06964668}
\elib{https://elibrary.ru/item.asp?id=28862967}


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  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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