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

Hamidur Rahman (hrahman***at***iitb.ac.in)
Ashutosh Mahajan (amahajan***at***iitb.ac.in)

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 programming, mixed-integer programming, convex hull, separation

Category 1: Global Optimization (Theory )

Category 2: Integer Programming ((Mixed) Integer Nonlinear Programming )

Citation: Industrial Engineering and Operations Research, IIT Bombay, July 2017

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Entry Submitted: 07/18/2017
Entry Accepted: 07/23/2017
Entry Last Modified: 03/01/2019

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