Testing the definiteness of matrices on polyhedral cones
type: Item
instance of: scholarly article
title: Testing the definiteness of matrices on polyhedral cones
zbMATH Open document ID: 0646.65039
published in: Linear Algebra and its Applications
publication date: 1988-01-01T00:00:00Z
review text: The author gives finite criteria for determining whether a real symmetric matrix is nonnegative definite, nonnegative definite plus, or positive definite on a convex polyhedral cone using the principal pivoting scheme for quadratic programming. Moreover, if a criterion gives an indication that a real symmetric matrix does not belong to a certain conditional definiteness class, the author shows how to determine a point in the polyhedral cone in which the definiteness class in question is violated. A procedure and some numerical examples are also given.
reviewed by: Florica Luban
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C20
zbMATH DE Number: 4054926
zbMATH Keywords: definiteness of matrices
zbMATH Keywords: convex polyhedral cone
zbMATH Keywords: principal pivoting scheme
zbMATH Keywords: quadratic programming
zbMATH Keywords: numerical examples
author: Hannu Väliaho
MaRDI profile type: Publication
cites work: Definiteness and semidefiniteness of quadratic forms revisited
cites work: Manifestations of the Schur complement
cites work: Q5625366
cites work: On classes of copositive matrices
cites work: Q5565769
cites work: A Principal Pivoting Simplex Algorithm for Linear and Quadratic Programming
cites work: On copositive matrices
cites work: Redundancy in mathematical programming. A state-of-the-art survey
cites work: The general quadratic optimization problem
cites work: Q4050723
cites work: Finite criteria for conditional definiteness of quadratic forms
cites work: Copositive matrices and definiteness of quadratic forms subject to homogeneous linear inequality constraints
cites work: Q3929386
cites work: Criteria for copositive matrices
cites work: A unified approach to one-parametric general quadratic programming
cites work: Q4118986
Recommended article: Almost definiteness of matrices on polyhedral cones
Recommended article: On a geometric property of positive definite matrices cone
Recommended article: On the cone of positive semidefinite matrices
Recommended article: On cone of nonsymmetric positive semidefinite matrices
Recommended article: Testing matrices for definiteness and application examples that spawn the need
Recommended article: Q3741734
Recommended article: Numerical test for semidefiniteness of functional matrices
Recommended article: On nonsingularity of a polytope of matrices
Recommended article: Cones of real positive semidefinite matrices associated with matrix stability
Recommended article: Q4937730
description: scientific article; zbMATH DE number 4054926