Tareq Hamadneh, "Computational Methods for Optimal Affine Bounds of Continuous Functions," WSEAS Transactions on Mathematics, vol. 25, pp. 51-56, 2026, DOI:10.37394/23206.2026.25.6
Tareq Hamadneh. Computational Methods for Optimal Affine Bounds of Continuous Functions.
WSEAS Transactions on Mathematics. 2026;25:51-56. 10.37394/23206.2026.25.6
WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 25, 2026
Computational Methods for Optimal Affine Bounds of Continuous Functions
Author:
Abstract: This paper presents global computational problems related to establishing lower bounds for
highdimensional continuous functions over a simplex. We propose a rigorous approach to constructing affine
lower bounds (ALB) that remain closely beneath the original function. By extending the least squares method for
control Bernstein, we develop a convergent AB to both polynomials and rational functions. Furthermore, we
demonstrate that these bounds achieve high convergence rates to the original functions. Finally, we evaluate our
approach by comparing it with previous methods using error bound approximation.
Keywords:
Global optimization, Bounding functions, Bernstein expansion, Polynomials, Minimization, simplices
Pages: 51-56 WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 25, 2026, Art. #6 DOI: 10.37394/23206.2026.25.6
×
Citation Tools