Revisiting k-sum optimization

In this paper, we address continuous, integer and combinatorial k -sum optimization problems. We analyze different formulations of this problem that allow to solve it through the minimization of a relatively small number of minisum optimization problems. This approach provides a general tool for solving a variety of k -sum optimization problems and at the same time, improves the complexity bounds of many ad-hoc algorithms previously reported in the literature for particular versions of this problem. Moreover, the results developed for k -sum optimization have been extended to the more general case of the convex ordered median problem, improving upon existing solution approaches.