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

Hamidur Rahman () and Ashutosh Mahajan ()
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Hamidur Rahman: Indian Institute of Technology Bombay
Ashutosh Mahajan: Indian Institute of Technology Bombay

Journal of Global Optimization, 2019, vol. 74, issue 3, No 1, 417-442

Abstract: 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.

Keywords: Bilinear constraints; Mixed-integer programming; Separation; Global optimization; Cutting-stock problem (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10898-019-00783-0

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