Journal of Global Optimization

, Volume 74, Issue 4, pp 705–735 | Cite as

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

  • Kedong Yan
  • Hong Seo RyooEmail author


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.


Logical analysis of data Pattern 0–1 multilinear programming Multi-term polyhedral relaxation Facet-defining inequalities Graph Star 


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer Science and Technology, School of Computer Science and EngineeringNanjing University of Science and TechnologyNanjingPeople’s Republic of China
  2. 2.School of Industrial Management EngineeringKorea UniversitySeoulSouth Korea

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