Solution Methods for Infinite-Dimensional Generalized Disjunctive Programming

What the math gives to ML

The strongest transferable asset is MBM-GP: replace expensive pointwise optimization of a domain-dependent relaxation bound with a Gaussian-process upper confidence envelope. In neural-network verification, ReLU and piecewise-linear activations are encoded by disjunctions whose big-M constants are activation bounds; these bounds vary over the input domain and can dominate verifier cost. A GP surrogate can learn bounds from a small set of exact bound solves, while an upper-confidence prediction remains conservative when calibrated. The practical first target is certified verification of small ReLU networks, measuring whether surrogate bounds reduce preprocessing and MILP solve time without increasing false certificates.