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

Kedong Yan, Hong Seo Ryoo

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)1-31
Number of pages31
JournalJournal of Global Optimization
DOIs
Publication statusAccepted/In press - 2018 Jun 25

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Learning systems
Term
Experiments
Polytope
Facet
Linear Inequalities
Machine Learning
Objective function
Numerical Experiment
Graph in graph theory
Logic

Keywords

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

ASJC Scopus subject areas

  • Computer Science Applications
  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

Cite this

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