A multi-term, polyhedral relaxation of a 0–1 multilinear function for Boolean logical pattern generation

Abstract

0–1 multilinear program (MP) holds a unifying theory to LAD pattern generation. This paper studies a multi-term relaxation of the objective function of the pattern generation MP for a tight polyhedral relaxation in terms of a small number of stronger 0–1 linear inequalities. Toward this goal, we analyze data in a graph to discover useful neighborhood properties among a set of objective terms around a single constraint term. In brief, they yield a set of facet-defining inequalities for the 0–1 multilinear polytope associated with the McCormick inequalities that they replace. The construction and practical utility of the new inequalities are illustrated on a small example and thoroughly demonstrated through numerical experiments with 12 public machine learning datasets.