MULTI-DIMENSIONAL SIMPLEXES IN THE PROBLEMS OF ECONOMICS


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Abstract

In order to expand the possibilities of numerical methods for solving nonlinear problems of mathematical programming in economics, it is proposed to use the «simplex» method. For this purpose, a generalization of the method, which found application in solving problems of determining local extrema of functions of two variables for the case of specifying functions in arbitrary n-dimensional spaces was made. Equilateral triangles are replaced by n-dimensional hypertetrahedra. An example of solving the problem of determining the local minimum of a function of three variables is given.

About the authors

Boris Alexeevich Gorlach

Samara National Research University

Author for correspondence.
Email: lioner97@mail.ru

Alexander Arkadyevich Rylov

Financial University under the Government of the Russian Federation

Email: lioner97@mail.ru

References

  1. Gorlach B.A. Matematicheskii analiz [Mathematical analysis]. SPb.: izd. «Lan’», 2013, 601 p. [in Russian].
  2. Gorlach B.A. Matematika [Mathematics]. M.: YuNITI-DANA, 2006, 911 p. [in Russian]
  3. Bakhvalov N.S., Zhidkov N.L. Chislennye metody [Numerical methods]. M.: Izd. «Laboratoriya Bazovykh Znanii», 2003, 632 p. [in Russian].

Copyright (c) 2018 Борис Алексеевич Горлач, Александр Аркадьевич Рылов

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