  Cutting planes for mixed-integer linear programs (MILPs) are typically
computed in rounds by iteratively solving optimization problems, the so-called
separation. Instead, we reframe the problem of finding good cutting planes as a
continuous optimization problem over weights parametrizing families of valid
inequalities. This problem can also be interpreted as optimizing a neural
network to solve an optimization problem over subadditive functions, which we
call the subadditive primal problem of the MILP. To do so, we propose a
concrete two-step algorithm, and demonstrate empirical gains when optimizing
generalized Gomory mixed-integer inequalities over various classes of MILPs.
Code for reproducing the experiments can be found at
https://github.com/dchetelat/subadditive.
