On the computation of C* certificates

Authors:
Florian Jarre;Katrin Schmallowsky
Affiliations:
Mathematisches Institut, University of Düsseldorf, Düsseldorf, Germany 40225;Mathematisches Institut, University of Düsseldorf, Düsseldorf, Germany 40225
Venue:
Journal of Global Optimization
Year:
2009

Citing 4
Cited 2

Some NP-complete problems in quadratic and nonlinear programming

Mathematical Programming: Series A and B
On Copositive Programming and Standard Quadratic Optimization Problems

Journal of Global Optimization
A linear programming reformulation of the standard quadratic optimization problem

Journal of Global Optimization
An Augmented Primal-Dual Method for Linear Conic Programs

SIAM Journal on Optimization

Think co(mpletely)positive ! Matrix properties, examples and a clustered bibliography on copositive optimization

Journal of Global Optimization
On the computational complexity of membership problems for the completely positive cone and its dual

Computational Optimization and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

The cone of completely positive matrices C* is the convex hull of all symmetric rank-1-matrices xx T with nonnegative entries. While there exist simple certificates proving that a given matrix $${B\in C^*}$$ is completely positive it is a rather difficult problem to find such a certificate. We examine a simple algorithm which--for a given input B--either determines a certificate proving that $${B\in C^*}$$ or converges to a matrix $${\bar S}$$ in C* which in some sense is "close" to B. Numerical experiments on matrices B of dimension up to 200 conclude the presentation.