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

Author

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  • 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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    1. Gabriela Alexe & Sorin Alexe & Peter Hammer & Bela Vizvari, 2006. "Pattern-based feature selection in genomics and proteomics," Annals of Operations Research, Springer, vol. 148(1), pages 189-201, November.
    2. Kedong Yan & Hong Seo Ryoo, 2017. "Strong valid inequalities for Boolean logical pattern generation," Journal of Global Optimization, Springer, vol. 69(1), pages 183-230, September.
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    5. Sorin Alexe & Eugene Blackstone & Peter Hammer & Hemant Ishwaran & Michael Lauer & Claire Pothier Snader, 2003. "Coronary Risk Prediction by Logical Analysis of Data," Annals of Operations Research, Springer, vol. 119(1), pages 15-42, March.
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