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：我们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 线性化的松弛同样强（Operations Research Letters 51 (2023) 146-152）。在本文中，我们将该结果推广至更一般的线性化，并给出一个更简洁的证明。此外，我们补充了 Khajavirad 的结果，证明了此类线性化松弛的交集与扩展花形松弛具有相同的强度。