Effective Separation of Disjunctive Cuts for Convex Mixed Integer Nonlinear Programs
The authors describe a computationally effective method for generating disjunctive inequalities for convex Mixed-Integer NonLinear Programs (MINLPs). The method relies on solving a sequence of cut-generating linear programs, and in the limit will generate an inequality as strong as can be produced by the cut-generating nonlinear program suggested by Stubbs and Mehrotra. Using this procedure, the authors are able to approximately optimize over the rank one simple disjunctive closure for a wide range of convex MINLP instances. The results indicate that disjunctive inequalities have the potential to close a significant portion of the integrality gap for convex MINLPs. In addition, they find that using this procedure within a branch-and-cut solver for convex MINLPs yields significant savings in total solution time for many instances.