An improved algorithm to test copositivity

Authors:
Julia Sponsel;Stefan Bundfuss;Mirjam Dür
Affiliations:
Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, Groningen, The Netherlands 9700 AK;, Heddesheim, Germany 68542;Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, Groningen, The Netherlands 9700 AK
Venue:
Journal of Global Optimization
Year:
2012

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Abstract

Copositivity plays a role in combinatorial and nonconvex quadratic optimization. However, testing copositivity of a given matrix is a co-NP-complete problem. We improve a previously given branch-and-bound type algorithm for testing copositivity and discuss its behavior in particular for the maximum clique problem. Numerical experiments indicate that the speedup is considerable.