On Computing the Copositive Minimum and its Representatives

Abstract

Computing the copositive minimum of a strictly copositive quadratic form is a natural generalization of computing the arithmetical minimum of a positive definite one. In this paper we show that this generalized problem is NP-complete. Moreover, we describe a practical method to calculate all shortest vectors using the LDLT-decomposition in a big class of special cases. Our numerical tests show that our method performs significantly better than previous approaches.