Piecewise Polyhedral Formulations for a Multilinear Term

In this paper, we present a mixed-integer linear programming formulation of a piecewise, polyhedral relaxation (PPR) of a multilinear term using it's convex hull representation. Based on the solution of the PPR, we also present a MIP-based piecewise formulation which restricts the solutions to be feasible for the multilinear term. We then present computational results showing the effectiveness of proposed formulations on instances from the standard Mixed-Integer Nonlinear Programming Library (MINLPLib) and compare the proposed formulation with a formulation that is built by recursively relaxing bilinear groupings of the multilinear term, typically applied in the literature.