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

Kedong Yan () and Hong Seo Ryoo ()
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Kedong Yan: Nanjing University of Science and Technology
Hong Seo Ryoo: Korea University

Journal of Global Optimization, 2019, vol. 74, issue 4, No 6, 705-735

Abstract: 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.

Keywords: Logical analysis of data; Pattern; 0–1 multilinear programming; Multi-term polyhedral relaxation; Facet-defining inequalities; Graph; Star (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10898-018-0680-8

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