We consider linear relaxations for multilinear optimization problems. In a recent paper, Khajavirad proved that the extended flower relaxation is at least as strong as the relaxation of any recursive McCormick linearization (Operations Research Letters 51 (2023) 146-152). In this paper we extend the result to more general linearizations, and present a simpler proof. Moreover, we complement Khajavirad's result by showing that the intersection of the relaxations of such linearizations and the extended flower relaxation are equally strong.

翻译：本文考虑多线性优化问题的线性松弛。在最近的一篇论文中，Khajavirad证明了扩展花形松弛至少与任何递归McCormick线性化的松弛强度相同（Operations Research Letters 51 (2023) 146-152）。本文将该结果推广到更一般的线性化，并给出了更简洁的证明。此外，我们补充了Khajavirad的结论，证明此类线性化松弛的交集与扩展花形松弛具有相同的强度。