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

Author

Listed:
  • Kedong Yan

    (Nanjing University of Science and Technology)

  • Hong Seo Ryoo

    (Korea University)

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.

Suggested Citation

  • Kedong Yan & Hong Seo Ryoo, 2019. "A multi-term, polyhedral relaxation of a 0–1 multilinear function for Boolean logical pattern generation," Journal of Global Optimization, Springer, vol. 74(4), pages 705-735, August.
    • Handle: RePEc:spr:jglopt:v:74:y:2019:i:4:d:10.1007_s10898-018-0680-8
    DOI: 10.1007/s10898-018-0680-8
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    References listed on IDEAS

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