When is rounding allowed? A new approach to integer nonlinear optimization

In this paper we present a new approach for solving unrestricted integer nonlinear programming problems. More precisely, we investigate in which cases one can solve the integer version of a nonlinear optimization problem by rounding (up or down) the components of a solution for its continuous relaxation. The idea is based on the level sets of the objective function. We are able to identify geometric properties of the level sets that ensure that such a rounding property holds. We illustrate that such properties of level sets can be found in typical problems of location theory.