Trust region algorithms for the nonlinear least distance problem
type: Item
instance of: scholarly article
title: Trust region algorithms for the nonlinear least distance problem
zbMATH Open document ID: 0830.65057
DOI: 10.1007/BF02143933
author: D. Zwick
author: Hans-Peter Helfrich
published in: Numerical Algorithms
publication date: 1996-02-04T00:00:00Z
review text: This paper discusses the nonlinear least distance problem, which is a special case of equality constrained optimization. Let a curve or surface be given in implicit form via the equation \(f(x)= 0\), \(x\in \mathbb{R}^d\), and let \(z\in \mathbb{R}^d\) be a fixed data point. This paper discusses two algorithms for solving the following problem: Find a point \(x^*\) such that \(f(x^*)= 0\) and \(|z- x^*|_2\) is minimal among all such \(x\). The algorithms presented use the trust region approach in which, at each iteration, an approximation to the objective function or merit function is given in the neighborhood (the trust region) of the current iterate. Among other things, this allows one to prove global convergence of the algorithm.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C20
zbMATH DE Number: 770303
zbMATH Keywords: trust region algorithms
zbMATH Keywords: nonlinear least distance problem
zbMATH Keywords: equality constrained optimization
zbMATH Keywords: global convergence
reviewed by: Nai-Yang Deng
MaRDI profile type: Publication
cites work: Q3690580
cites work: Q3681854
cites work: Q3330984
cites work: Q4226179
cites work: A trust region method for implicit orthogonal distance regression
cites work: Q4083217
cites work: A trust region algorithm for equality constrained optimization
full work available at URL: https://doi.org/10.1007/bf02143933
OpenAlex ID: W1968077169
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description: scientific article; zbMATH DE number 770303