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

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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.

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Authors and Affiliations

  1. Department of Computer Science and Technology, School of Computer Science and Engineering, Nanjing University of Science and Technology, 200 Xiaolingwei, Xuanwu District, Nanjing, 210094, Jiangsu, People’s Republic of China

    Kedong Yan

  2. School of Industrial Management Engineering, Korea University, 145 Anam-Ro, Seongbuk-Gu, Seoul, 02841, South Korea

    Hong Seo Ryoo

Authors
  1. Kedong Yan
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  2. Hong Seo Ryoo
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Correspondence to Hong Seo Ryoo.

Additional information

Kedong Yan: Most of the research in this paper was conducted while this author was at Korea University.

This work was supported by Samsung Science and Technology Foundation under Project Number SSTF-BA1501-03.

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Yan, K., Ryoo, H.S. A multi-term, polyhedral relaxation of a 0–1 multilinear function for Boolean logical pattern generation. J Glob Optim 74, 705–735 (2019). https://doi.org/10.1007/s10898-018-0680-8

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  • DOI: https://doi.org/10.1007/s10898-018-0680-8

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