Relaxation strength for multilinear optimization: McCormick strikes back
This work addresses theoretical improvements in relaxation methods for multilinear optimization, offering incremental advances in mathematical optimization.
The paper extends a previous result showing that the extended flower relaxation is at least as strong as recursive McCormick linearizations for multilinear optimization, providing a simpler proof and proving that their intersection yields equally strong relaxations.
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.