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Compact linearization for binary quadratic problems subject to assignment constraints

Sven Mallach ()
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Sven Mallach: Universität zu Köln

4OR, 2018, vol. 16, issue 3, 295-309

Abstract: Abstract We introduce and prove new necessary and sufficient conditions to carry out a compact linearization approach for a general class of binary quadratic problems subject to assignment constraints that has been proposed by Liberti (4OR 5(3):231–245, 2007, https://doi.org/10.1007/s10288-006-0015-3 ). The new conditions resolve inconsistencies that can occur when the original method is used. We also present a mixed-integer linear program to compute a minimally sized linearization. When all the assignment constraints have non-overlapping variable support, this program is shown to have a totally unimodular constraint matrix. Finally, we give a polynomial-time combinatorial algorithm that is exact in this case and can be used as a heuristic otherwise.

Keywords: Non-linear programming; Binary quadratic programming; Mixed-integer programming; Linearization; 68R01; 90C05; 90C09; 90C10; 90C11; 90C20; 90C30 (search for similar items in EconPapers)
Date: 2018
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