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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)
In this paper we consider an aggregation technique introduced by Yıldıran [45] to study the convex hull of regions defined by two quadratic or by a conic quadratic and a quadratic inequality. Yıldıran [45] shows how to characterize the convex hull of open sets defined by two strict quadratic inequalities using Linear Matrix Inequalities (LMI). We show how(More)
Today, having a strong social media presence is an important issue for large and small companies. A key social media challenge faced by these companies' marketing teams is how to maximize the impressions or views of the content they post in a social network. Optimizing the posting time of content to increase impressions is an approach not considered before(More)
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