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We study the generalization of split, k-branch split, and intersection cuts from Mixed Integer Linear Programming to the realm of Mixed Integer Nonlinear Programming. Constructing such cuts requires calculating the convex hull of the difference between a convex set and an open set with a simple geometric structure. We introduce two techniques to give(More)
We study split cuts and extended formulations for Mixed Integer Conic Quadratic Programming (MICQP) and their relation to Conic Mixed Integer Rounding (CMIR) cuts. We show that CMIR is a linear split cut for the polyhedral portion of an extended formulation of a quadratic set and it can be weaker than the nonlinear split cut of the same quadratic set.(More)
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