A standard quadratic problem consists of nding global maximizers of a quadratic form over the standard simplex. In this paper, the usual semideenite programming relaxation is strengthened by… (More)

We study linear optimization problems over the cone of copositive matrices. These problems appear in nonconvex quadratic and binary optimization; for instance, the maximum clique problem and other… (More)

Copositive programming is a relatively young field in mathematical optimization. It can be seen as a generalization of semidefinite programming, since it means optimizing over the cone of so called… (More)

Depth-first simplicial partition for copositivity detection, with an application to MaxClique Julius Žilinskas a & Mirjam Dür b a Institute of Mathematics and Informatics , Vilnius University ,… (More)

A matrix X is called completely positive if it allows a factorisation X = ∑ b∈B bb T with nonnegative vectors b. These matrices are of interest in optimisation, as it has been found that several… (More)

We describe the main open problems which are currently of interest in the theory of copositive and completely positive matrices. We give motivation as to why these questions are relevant and provide… (More)