In this paper, we present a mixed-integer linear programming (MILP) formulation of a piecewise, polyhedral relaxation (PPR) of a multilinear term using its convex hull representation. Based on the solution of the PPR, we also present a MILP formulation whose solutions are feasible for nonconvex, multilinear equations. We then present computational results showing the effectiveness of proposed formulations on instances of standard benchmarks of nonlinear programs (NLPs) with multilinear terms and compare the proposed formulation with a traditional formulation that is built by recursively relaxing bilinear groupings of multilinear terms.

中文翻译：

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多线性项的分段多面体公式

在本文中，我们提出了使用凸包表示的多线性项的分段多面体松弛 (PPR) 的混合整数线性规划 (MILP) 公式。基于 PPR 的解，我们还提出了一个 MILP 公式，其解对于非凸多线性方程是可行的。然后，我们展示了计算结果，显示了所提出的公式对具有多线性项的非线性程序 (NLP) 的标准基准实例的有效性，并将所提出的公式与通过递归松弛多线性项的双线性分组构建的传统公式进行比较。