On a subproblem of trust region algorithms for constrained optimization
type: Item
instance of: scholarly article
title: On a subproblem of trust region algorithms for constrained optimization
zbMATH Open document ID: 0711.90062
DOI: 10.1007/BF01580852
published in: Mathematical Programming. Series A. Series B
publication date: 1990-01-01T00:00:00Z
review text: The author studies a subproblem which appears in some trust region algorithms for constrained optimization, where the original problem is to minimize a nonlinear function subject to equality constraints. It is the minimization of a general quadratic function with two special quadratic constraints. Some peculiarities of the problem, mainly with respect to the signs of the eigenvalues of the Hessian of the Lagrangian function at a solution are investigated. The main result is that the Hessian of the Lagrangian has at most one negative eigenvalue if the Lagrangian multipliers are unique. An example is presented to show that the Hessian may have a negative eigenvalue when one constraint is inactive at the solution.
Mathematics Subject Classification ID: 90C20
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90-08
Mathematics Subject Classification ID: 90C30
zbMATH DE Number: 4170649
zbMATH Keywords: trust region algorithms
zbMATH Keywords: constrained optimization
zbMATH Keywords: equality constraints
zbMATH Keywords: quadratic function
zbMATH Keywords: signs of the eigenvalues
zbMATH Keywords: Hessian of the Lagrangian function
author: Yaxiang Yuan
reviewed by: Maxim Ivanov Todorov
describes a project that uses: GQTPAR
MaRDI profile type: Publication
cites work: Q3681854
cites work: Q3928936
cites work: Computing Optimal Locally Constrained Steps
cites work: Computing a Trust Region Step
cites work: A trust region algorithm for equality constrained optimization
full work available at URL: https://doi.org/10.1007/bf01580852
OpenAlex ID: W2010364290
description: scientific article; zbMATH DE number 4170649