On Lagrange multipliers of trust-region subproblems
type: Item
instance of: scholarly article
title: On Lagrange multipliers of trust-region subproblems
zbMATH Open document ID: 1163.90027
published in: BIT
publication date: 2009-04-29T00:00:00Z
full work available at URL: http://hdl.handle.net/10338.dmlcz/702866
review text: Due to their good convergence properties, trust-region methods are widely used. When computing the next iterate, one solves an unconstrained trust-region subproblem that involves also Lagrange multipliers. Several solution approaches, as for example the Steihaug-Toint CG method [\textit{T. Steihaug}, SIAM J. Numer. Anal. 20, 626--637 (1983; Zbl 0518.65042); \textit{Ph. L. Toint}, in: Proc. IMANA Conf., Reading 1980, 57--88 (1981; Zbl 0463.65045)] only require approximations of the Lagrange multipliers. This paper proves a property of the Lagrange multipliers generated when using a Krylov subspace method for the solution of the subproblems. That is, it is shown that the Lagrange multipliers grow monotonically. The paper also suggests improved solution techniques that take this additional property of the Lagrange multipliers into account.
reviewed by: Andrea Walther
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 49M29
zbMATH DE Number: 5549589
zbMATH Keywords: trust region subproblem
zbMATH Keywords: Lagrange multipliers
zbMATH Keywords: Krylov spaces
author: Ladislav Lukšan
author: Ctirad Matonoha
author: Jan Vlček
describes a project that uses: GQTPAR
describes a project that uses: HSL-VF05
MaRDI profile type: Publication
OpenAlex ID: W2101734906
cites work: Solving the Trust-Region Subproblem using the Lanczos Method
cites work: Computing a Trust Region Step
cites work: The Conjugate Gradient Method and Trust Regions in Large Scale Optimization
cites work: Q3914337
DOI: 10.1007/S10543-008-0197-5
description: scientific article; zbMATH DE number 5549589