Variational analysis of an extended eigenvalue problem
type: Item
instance of: scholarly article
title: Variational analysis of an extended eigenvalue problem
zbMATH Open document ID: 0823.15008
DOI: 10.1016/0024-3795(92)00016-F
author: Yanyan Li
published in: Linear Algebra and its Applications
publication date: 1995-11-07T00:00:00Z
review text: This paper considers for a symmetric matrix \(B\) the problem: maximize \(\mu_ a : = x^ tBx - 2a^ tx\) subject to \(x^ tx = 1\). For the solution it is necessary to computers the Lagrange multiplier \(\lambda (a)\) as extended eigenvalue \(\lambda (a) = \max \{\lambda \mid (B - \lambda I)x = a\); \(x^ tx = 1\}\) of the pair \(\{B,a\}\). Nonsmooth analysis is required to discuss the function \(\lambda(a)\) in order to derive a multiplier result on the sensitivity near 0. The authors prove continuous differentiability on a large set of points and that \(\lambda (\cdot)\) is Lipschitz near 0 and regular at 0. They characterize the generalized gradient and directional derivatives at 0.
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C20
zbMATH DE Number: 769036
zbMATH Keywords: mathematical programming
zbMATH Keywords: extended eigenvalue problem
zbMATH Keywords: quadratic problem
zbMATH Keywords: nonsmooth analysis
zbMATH Keywords: symmetric matrix
zbMATH Keywords: Lagrange multiplier
reviewed by: W. Gander
describes a project that uses: GQTPAR
MaRDI profile type: Publication
cites work: Q3324260
cites work: Q4000274
cites work: Q4226179
cites work: On the Stationary Values of a Second-Degree Polynomial on the Unit Sphere
cites work: Least squares with a quadratic constraint
cites work: A constrained eigenvalue problem
cites work: Some Modified Matrix Eigenvalue Problems
cites work: Quadratically constrained least squares and quadratic problems
cites work: Computing a Trust Region Step
cites work: Newton’s Method with a Model Trust Region Modification
cites work: Trust Region Problems and Nonsymmetric Eigenvalue Perturbations
description: scientific article; zbMATH DE number 769036