Performance comparison of two recently proposed copositivity tests

Recently and simultaneously, two MILP-based approaches to copositivity testing were proposed. This note tries a performance comparison, using a group of test sets containing a large number of designed instances. According to the numerical results, we find that one copositivity detection approach performs better when the function value of the defined function h of a matrix is large while the other one performs better when the dimension of problems is increasing moderately. A problem set that is hard for both approaches is also presented, which may be used as a test bed for future competing approaches. An improved variant of one of the approaches is also proposed to handle those hard instances more efficiently.