Algorithms for projecting a point onto a level surface of a continuous function on a compact set
type: Item
instance of: scholarly article
title: Algorithms for projecting a point onto a level surface of a continuous function on a compact set
zbMATH Open document ID: 1331.65043
DOI: 10.1134/S0965542514090036
author: N. K. Arutyunova
author: A. M. Dulliev
author: V. I. Zabotin
published in: Computational Mathematics and Mathematical Physics
publication date: 2015-11-06T00:00:00Z
review text: The paper deals with the problem of finding a solution nearest to a given point for the equation \(f(x) = 0\), where \(f\) is an \(\varepsilon\)-Lipschitz continuous function. To solve the problem the authors propose two algorithms. The first algorithm is based on an idea similar to the second algorithm from \textit{V. I. Zabotin} and \textit{N. K. Arutyunova} [Zh. Vychisl. Mat. Mat. Fiz. 53, No. 3, 344--349 (2013; Zbl 1274.65065)]. It is an iterative algorithm in which the convergence to the set of zeros for the function is obtained by updating the value of \(\varepsilon\) depending on the current value of the function. The second algorithm is a generalization of the method from \textit{A. M. Dulliev} and \textit{V. I. Zabotin} [Zh. Vychisl. Mat. Mat. Fiz. 44, No. 5, 827--830 (2004); translation in Comput. Math. Math. Phys. 44, No. 5, 781--784 (2004; Zbl 1121.41034)]. After the introduction of the two algorithms the authors prove their convergence and show some numerical examples.
reviewed by: Krzysztof Gdawiec
Mathematics Subject Classification ID: 65D18
Mathematics Subject Classification ID: 65H05
zbMATH DE Number: 6505303
zbMATH Keywords: nonlinear equation
zbMATH Keywords: \(\varepsilon\)-Lipschitz continuity
zbMATH Keywords: projection of a point onto a level surface
zbMATH Keywords: nonconvex set
zbMATH Keywords: algorithm
zbMATH Keywords: convergence
zbMATH Keywords: numerical example
MaRDI profile type: Publication
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full work available at URL: s0965542514090036
OpenAlex ID: W1983594931
description: scientific article; zbMATH DE number 6505303