On pathological disjunctions and redundant disjunctive conic cuts

The development of Disjunctive Conic Cuts (DCCs) for Mixed Integer Second Order Cone Optimization (MISOCO) problems has recently gained significant interest in the optimization community. In this paper, we explore the pathological disjunctions where disjunctive cuts do not tighten the description of the feasible set. We focus on the identification of cases when the generated DCCs are redundant. Avoiding the generation of redundant cuts saves computational time and facilitates efficient implementation of branch and cut algorithms.