A new semidefinite programming bound for indefinite quadratic forms over a simplex
type: Item
instance of: scholarly article
title: A new semidefinite programming bound for indefinite quadratic forms over a simplex
zbMATH Open document ID: 0959.65077
DOI: 10.1023/A:1008315627883
author: Ivo Nowak
published in: Journal of Global Optimization
publication date: 1999-09-22T00:00:00Z
review text: The author describes a method for computing a lower bound of the minimum of an indefinite quadratic form \(f(x):= x^T Fx\) over the \(n\)-dimensional standard simplex \(\Delta_n\). This method requires two steps. Firstly, by solving a certain semidefinite program there is found a symmetric matrix \(W\) which satisfies \(W\leq F\) (componentwise) and for which the quadratic form \(w(x):= x^T Wx\) is convex on \(\Delta_n\). Secondly, the minimum of \(w\) over \(\Delta_n\) is determined. It is proved that this minimum is a lower bound of the minimum of \(f\) over \(\Delta_n\).
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C22
Mathematics Subject Classification ID: 90C20
Mathematics Subject Classification ID: 90C26
zbMATH DE Number: 1339671
zbMATH Keywords: semidefinite programming
zbMATH Keywords: quadratic programming
zbMATH Keywords: indefinite quadratic form
reviewed by: Wolfgang W. Breckner
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1339671