  We propose an analytic center cutting plane method to determine if a matrix
is completely positive, and return a cut that separates it from the completely
positive cone if not. This was stated as an open (computational) problem by
Berman, D\"ur, and Shaked-Monderer [Electronic Journal of Linear Algebra,
2015]. Our method optimizes over the intersection of a ball and the copositive
cone, where membership is determined by solving a mixed-integer linear program
suggested by Xia, Vera, and Zuluaga [INFORMS Journal on Computing, 2018]. Thus,
our algorithm can, more generally, be used to solve any copositive optimization
problem, provided one knows the radius of a ball containing an optimal
solution. Numerical experiments show that the number of oracle calls (matrix
copositivity checks) for our implementation scales well with the matrix size,
growing roughly like $O(d^2)$ for $d\times d$ matrices. The method is
implemented in Julia, and available at
https://github.com/rileybadenbroek/CopositiveAnalyticCenter.jl.
