New zero-finders for trust-region computations
type: Item
instance of: scholarly article
title: New zero-finders for trust-region computations
zbMATH Open document ID: 1394.65040
author: Maged Alkilayh
author: Jinyun Yuan
author: Lothar Reichel
published in: Numerical Algorithms
publication date: 2017-11-17T00:00:00Z
review text: Trust-region methods are among the most popular schemes when solving optimization problems. An important part of each trust-region method is determination of a direction vector. It is a unique minimum of a quadratic function that approximates the function to be minimized on the set called the trust-region. This direction vector depends on a parameter that is determined by applying the Newton method for the computation of the zero of a certain nonlinear function representing the distance of the direction vector from the trust-region. Several known zero-finders that exhibit quadratic convergence are described in the paper. Then, the authors bring two new zero-finders that yield cubic convergence and only require insignificantly additional computational work per step than the quadratically convergent zero-finders described. It is based on the observation that the second derivative of the corresponding function can be evaluated inexpensively when the first derivative is known. The new zero-finders are first discussed in the context of determining a zero of a fairly general function with two continuous derivatives and at least one zero. Then, the application to the trust-region computation is discussed.
reviewed by: Ctirad Matonoha
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 49M15
Mathematics Subject Classification ID: 49M37
zbMATH DE Number: 6808520
zbMATH Keywords: zero-finder
zbMATH Keywords: trust region subproblem
zbMATH Keywords: cubic convergence
zbMATH Keywords: optimization
zbMATH Keywords: Newton's method
zbMATH Keywords: nonlinear equations
describes a project that uses: GQTPAR
MaRDI profile type: Publication
full work available at URL: s11075-016-0260-2
OpenAlex ID: W2567302026
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DOI: 10.1007/S11075-016-0260-2
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description: scientific article; zbMATH DE number 6808520