Piecewise Polyhedral Formulations for a Multilinear Term

TL;DR

This paper introduces a novel MILP formulation for multilinear terms using piecewise polyhedral relaxations based on convex hulls, improving solution feasibility and efficiency for nonlinear programming problems.

Contribution

It presents a new MILP formulation for multilinear terms that leverages convex hull representations and compares it with traditional relaxation methods.

Findings

The proposed formulation improves solution feasibility for nonconvex multilinear equations.

Computational results show enhanced performance on benchmark nonlinear programs.

The method outperforms traditional recursive relaxation approaches.

Abstract

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.