A convex reformulation and an outer approximation for a class of binary quadratic program
Borzou Rostami, Fausto Errico, Andrea Lodi · PolyPublie (École Polytechnique de Montréal) · 2018
In this paper, we propose a general modeling framework for a large class of binary quadratic programs subject to variable partitioning constraints.This problem has a wide range of applications as many of the binary quadratic programs with linear constraints can be represented in this form.By exploiting the problems' structure, we propose mixed-integer nonlinear program (MINLP) and mixed-integer linear program (MILP) reformulations and show the relationship between the two models in terms of the relaxation strength.Our methodology relies on a convex reformulation of the proposed MINLP and a branch-and-cut algorithm based on outer approximation cuts where the cuts are generated on the fly by efficiently solving separation subproblems.Our experimental results on various quadratic combinatorial optimization problems show that our approach outperforms the state-of-the-art solver applied to different MILP reformulations of the corresponding problems.