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Facets of a mixed-integer bilinear covering set with bounds on variables

Authors
  • Rahman, Hamidur1
  • Mahajan, Ashutosh1
  • 1 Indian Institute of Technology Bombay, Industrial Engineering and Operations Research, Mumbai, 400 076, India , Mumbai (India)
Type
Published Article
Journal
Journal of Global Optimization
Publisher
Springer US
Publication Date
May 14, 2019
Volume
74
Issue
3
Pages
417–442
Identifiers
DOI: 10.1007/s10898-019-00783-0
Source
Springer Nature
Keywords
License
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Abstract

We derive a closed form description of the convex hull of mixed-integer bilinear covering set with bounds on the integer variables. This convex hull description is determined by considering some orthogonal disjunctive sets defined in a certain way. This description does not introduce any new variables, but consists of exponentially many inequalities. An extended formulation with a few extra variables and much smaller number of constraints is presented. We also derive a linear time separation algorithm for finding the facet defining inequalities of this convex hull. We study the effectiveness of the new inequalities and the extended formulation using some examples.

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