Approximation of the Constant in a Markov-Type Inequality on a Simplex Using Meta-Heuristics

Grzegorz Sroka and Mariusz Oszust
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Grzegorz Sroka: Department of Topology and Algebra, Rzeszow University of Technology, Powstancow Warszawy 12, 35-959 Rzeszow, Poland
Mariusz Oszust: Department of Computer and Control Engineering, Rzeszow University of Technology, Wincentego Pola 2, 35-959 Rzeszow, Poland

Mathematics, 2021, vol. 9, issue 3, 1-10

Abstract: Markov-type inequalities are often used in numerical solutions of differential equations, and their constants improve error bounds. In this paper, the upper approximation of the constant in a Markov-type inequality on a simplex is considered. To determine the constant, the minimal polynomial and pluripotential theories were employed. They include a complex equilibrium measure that solves the extreme problem by minimizing the energy integral. Consequently, examples of polynomials of the second degree are introduced. Then, a challenging bilevel optimization problem that uses the polynomials for the approximation was formulated. Finally, three popular meta-heuristics were applied to the problem, and their results were investigated.

Keywords: minimal polynomials; complex equilibrium measure; Markov’s inequality; bilevel optimization; optimization methods (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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