A continuation method for solving fixed points of self-mappings in general nonconvex sets
type: Item
instance of: scholarly article
title: A continuation method for solving fixed points of self-mappings in general nonconvex sets
zbMATH Open document ID: 1020.65030
DOI: 10.1016/S0362-546X(02)00140-2
author: Zhenghua Lin
author: Bo Yu
author: Daoli Zhu
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-03-11T00:00:00Z
review text: For the computation of fixed points of a sufficiently differentiable mapping from a non-convex, bounded subset \(\Omega \subset \mathbb{R}^n\) into itself, \textit{Z. Lin} and \textit{B. Yu} [Appl. Math. Comput. 74, 66-77 (1996; Zbl 0840.65038)] introduced a combined homotopy and interior-point method and proved for a class of sets \(\Omega\) that for almost all starting points, there exist regular solution curves of a specific homotopy which, in a certain sense, tend to the fixed point set. In this paper it is shown that the result remains valid under somewhat weakened conditions on the class of sets.
Mathematics Subject Classification ID: 65H20
Mathematics Subject Classification ID: 65H10
zbMATH DE Number: 1879986
zbMATH Keywords: fixed point
zbMATH Keywords: non-convex set
zbMATH Keywords: homotopy method
zbMATH Keywords: self-mapping
zbMATH Keywords: continuation method
zbMATH Keywords: interior-point method
reviewed by: Werner C. Rheinboldt
MaRDI profile type: Publication
cites work: Q3998344
cites work: Finding Zeroes of Maps: Homotopy Methods That are Constructive With Probability One
cites work: Existence of an interior pathway to a Karush-Kuhn-Tucker point of a nonconvex programming problem
cites work: A Constructive Proof of the Brouwer Fixed-Point Theorem and Computational Results
cites work: A combined homotopy interior point method for convex nonlinear programming
cites work: Homotopy method for a class of nonconvex Brouwer fixed-point problems
full work available at URL: s0362-546x(02)00140-2
OpenAlex ID: W2020401288
description: scientific article; zbMATH DE number 1879986