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

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  • Hamidur Rahman

    (Indian Institute of Technology Bombay)

  • Ashutosh Mahajan

    (Indian Institute of Technology Bombay)

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.

Suggested Citation

  • Hamidur Rahman & Ashutosh Mahajan, 2019. "Facets of a mixed-integer bilinear covering set with bounds on variables," Journal of Global Optimization, Springer, vol. 74(3), pages 417-442, July.
    • Handle: RePEc:spr:jglopt:v:74:y:2019:i:3:d:10.1007_s10898-019-00783-0
    DOI: 10.1007/s10898-019-00783-0
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    References listed on IDEAS

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    Cited by:

    1. Hamidur Rahman & Ashutosh Mahajan, 2020. "On the facet defining inequalities of the mixed-integer bilinear covering set," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(3), pages 545-575, December.

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