  This paper aims to answer an open question recently posed in the literature,
that is to find a fast exact method for solving the p-dispersion-sum problem
(PDSP), a nonconcave quadratic binary maximization problem. We show that, since
the Euclidean distance matrix defining the quadratic term in (PDSP) is always
conditionally negative definite, the cutting plane method is exact for (PDSP)
even in the absence of concavity. As such, the cutting plane method, which is
primarily designed for concave maximisation problems, converges to the optimal
solution of the (PDSP). The numerical results show that the method outperforms
other exact methods for solving (PDSP), and can solve to optimality large
instances of up to two thousand variables.
