Compact Linearization for Binary Quadratic Problems subject to Linear Equations

Abstract: In this paper it is shown that the compact linearization approach, that has been previously proposed only for binary quadratic problems with assignment constraints, can be generalized to arbitrary linear equations with positive coefficients which considerably enlarges its applicability. We discuss special cases of prominent quadratic combinatorial optimization problems where the obtained compact linearization yields a continuous relaxation that is provably as least as strong as the one obtained with an ordinary linearization.