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

Hamidur Rahman; Ashutosh Mahajan

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arXiv · 1707.06712

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

Hamidur Rahman·Ashutosh Mahajan

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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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BibTeX RIS

Hamidur Rahman, Ashutosh Mahajan. 2019-03-02. Facets of a mixed-integer bilinear covering set with bounds on variables. https://arxiv.org/abs/1707.06712

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