On a hierarchy of polytopes for integer quadratic programming

Galli, Laura and Letchford, Adam (2025) On a hierarchy of polytopes for integer quadratic programming. In: Mathematics, Algorithms and the Art and Science of Decision-Making :. Springer. (In Press)

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Abstract

A folklore result in integer programming is that bounded integer variables can be replaced with binary variables, using bit representation. Under certain conditions, this can be used to reformulate mixed-integer quadratic programs as mixed-integer linear programs, and thereby render them easier to solve. In fact, several reformulation strategies can be found in the literature. We conduct a systematic comparison of these strategies by focusing on integer quadratic programs with box constraints, and present a hierarchy for the associated polytopes.