A Polyhedral Characterization of Linearizable Quadratic Combinatorial Optimization Problems
Publication Date
12-15-2025
Description
We introduce a polyhedral framework for characterizing instances of quadratic combinatorial optimization problems (QCOPs) as being linearizable, meaning that the quadratic objective can be equivalently rewritten as linear in such a manner that preserves the objective function value at all feasible solutions. In particular, we show that an instance is linearizable if and only if the quadratic cost coefficients can be used to construct a linear equation, in a lifted variable space, that is valid for the affine hull of a specially structured discrete set. In addition to developing this result for general QCOPs, we illustrate its utility in the specific context of the quadratic minimum spanning tree problem (QMSTP). As a consequence of this new polyhedral perspective on the concept of linearizability, we are able to make progress on a recent open question regarding linearizable QMSTP instances defined on biconnected graphs.
Journal
Discrete Applied Mathematics
Volume
376
First Page
281
Last Page
293
Department
Mathematics
Link to Published Version
https://www.sciencedirect.com/science/article/abs/pii/S0166218X25003373?via%3Dihub
DOI
https://doi.org/10.1016/j.dam.2025.06.035
Recommended Citation
Waddell, Lucas. "A Polyhedral Characterization of Linearizable Quadratic Combinatorial Optimization Problems." (2025) : 281-293.