@article {8162,
	title = {Copositivity tests based on the Linear Complementarity Problem},
	journal = {Computational Optimization and Applications},
	volume = {63},
	year = {2016},
	pages = {461-- 493},
	abstract = {<p>We present copositivity tests based on new necessary and sufficient conditions which require the solution of linear complementarity problems (LCP). We propose methodologies involving Lemke{\textquoteright}s method, an enumerative algorithm and a linear mixed-integer programming formulation to solve the required LCPs. Moreover, we discuss a new necessary condition for (strict) copositivity based on solving a linear program, which can be used as a preprocessing step. The algorithms with these three different variants are thoroughly applied to test matrices from the literature and to max-clique instances with matrices of order up to 496{\texttimes}496. We compare our procedures with three other copositivity tests from the literature as well as with a general global optimization solver. The numerical results are very promising and equally good and in many cases better than the results reported elsewhere.</p>
},
	url = {http://link.springer.com/article/10.1007/s10589-015-9772-2},
	author = {C. Br{\'a}s and G. Eichfelder and J{\'u}dice, J.}
}
