A Mixed Integer Second Order Cone Optimization (MISOCO) problem minimizes a linear function over the set of solutions of a system of linear equations and the Cartesian product of second order cones of various dimensions, where a subset of the variables is constrained to be integer. In this work we study the derivation of novel Disjunctive Conic Cuts (DCCs) for MISOCO problems. Our main goal is to extend the ideas of disjunctive programming that have shown to be successful in the derivation of linear cuts for mixed integer linear optimization. Here, we describe how this ideas can be applied to MISOCO problems for generating conic cuts. Additionally, we present some preliminary numerical results that show that this cuts used in a branch-and-cut framework can effectively help to improve the solution process.

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