Convex Hull Formulations for Mixed-Integer Multilinear Functions

TL;DR

This paper introduces convex hull formulations for mixed-integer multilinear functions, providing improved relaxations that enhance solution quality in optimization problems involving products of continuous and binary variables.

Contribution

The paper develops two equivalent convex relaxations for MIMFs and analyzes their polyhedral properties, outperforming existing relaxation methods.

Findings

Proposed formulations outperform state-of-the-art relaxations

Convex relaxations improve solution bounds for MIMFs

Polyhedral analysis confirms the strength of the new formulations

Abstract

In this paper, we present convex hull formulations for a mixed-integer, multilinear term/function (MIMF) that features products of multiple continuous and binary variables. We develop two equivalent convex relaxations of an MIMF and study their polyhedral properties in their corresponding higher-dimensional spaces. We numerically observe that the proposed formulations consistently perform better than state-of-the-art relaxation approaches.