The reformulation-linearization-technique (RLT) is a well-known strengthening technique for binary mixed-integer optimization. It is well known to dominate lift-and-project strengthening, which is based on disjunctive programming (DP) for single-variable disjunctions. In contrast to the latter, the geometry of RLT is not understood completely. We provide some insights by characterizing the points in the corresponding RLT closure geometrically. We exploit this insight to show that RLT even dominates DP approaches based on cardinality equations with right-hand side 1. This is in contrast to cardinality inequalities with right-hand side 1, whose DPs are not dominated. Our results have applications in the strength comparison for the quadratic assignment problem.

翻译：重构线性化技术（RLT）是二元混合整数优化中一种广为人知的强化方法。众所周知，它支配着基于单变量析取的析取规划（DP）的提升投影强化方法。与后者不同，RLT的几何性质尚未被完全理解。我们通过几何刻画相应RLT闭包中的点，提供了一些见解。利用这一见解，我们证明RLT甚至支配基于右侧为1的基数方程的DP方法。这与右侧为1的基数不等式形成对比，后者的DP方法不受支配。我们的结果在二次分配问题的强度比较中具有应用价值。