Intersection Disjunctions for Reverse Convex Sets

We present a framework to obtain valid inequalities for reverse convex set: the set of points in polyhedron that lie outside given open set. Reverse sets arise many models, including bilevel optimization and polynomial optimization. An intersection cut is well-known inequality generated from basic solution lies within introduce deriving solutions first propose an extension cuts defines two-term disjunction set, which we refer as disjunction. Next, generalize this analysis multiterm by considering set’s recession directions. These disjunctions can be used cut-generating linear program