Recursive McCormick relaxations

Relaxation strength for multilinear optimization: McCormick strikes back

  • Matthias Walter
    • Categories (Mixed) Integer Linear Programming, Nonlinear Optimization, Polyhedra Tags , , , , ,

    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, … Read more

    On the strength of recursive McCormick relaxations for binary polynomial optimization

  • Aida Khajavirad
    • Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches, Integer Programming Tags , , , ,

    Recursive McCormick relaxations have been among the most popular convexification techniques for binary polynomial optimization problems. It is well-understood that both the quality and the size of these relaxations depend on the recursive sequence and finding an optimal recursive sequence amounts to solving a difficult combinatorial optimization problem. In this paper, we prove that any … Read more