Professional paper

On a global optimization problem

Petra Corn orcid.org/0000-0002-0895-8710 ; Odjel za matematiku, Sveučilište J.J. Strossmayera u Osijeku
Rudolf Scitovski ; Odjel za matematiku, Sveučilište J.J. Strossmayera u Osijeku

Abstract

We consider the following global optimization problem
\[\argmin\limits_{a\in\mathbb{R}^n}F(a),\quad F(a)=\int\limits_0^{+\infty}e^{-x}\left(1+a_1x+\cdots+a_nx^n\right)^2dx. \]
It is shown that {this problem has a unique solution, which can be determined by solving the corresponding least squares problem or as a special case of a general best approximation problem} in a unitary vector space. In the latter case, Laguerre polynomials are applied. The problem solving is illustrated by several numerical examples.

Keywords

global optimization; least squares problem; best approximation; Laguerre polynomials

Hrčak ID:

135196

URI

https://hrcak.srce.hr/135196

Publication date:

2.3.2015.

Article data in other languages: croatian

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