Disjunctive constraints appear naturally in a large variety of different mixed-integer optimization problems. Such problems include classical OR applications but also applications in AI and ML, e.g., clustering and optimization over ReLU DNNs. The classical modelling approaches for disjunctive constraints can result in very weak continuous relaxations or strong but computationally very challenging relaxations.

In this talk we discuss a new class of formulation called p-split formulations, that combines the advantages of big-M and convex hull formulations. The p-split formulations offers an adjustable type of formulation that can easily be adjusted towards a stronger convex relaxation at the expense of a more complex formulation or towards a simpler formulation. The advantage of the simpler formulations is mainly that the subproblems in branch-and-bound can be solved much faster, but at the expense of a potentially larger BB tree. Technical details and theoretical properties of the formulations are presented along with computational results.