Pietro Belotti, Visiting Assistant Professor, Lehigh University

Mixed-Integer Nonlinear Programming (MINLP) problems present two main challenges: the integrality of a subset of variables and non-convex (nonlinear) objective function and constraints. Both types of non-convexity can be dealt with by applying, explicitly or implicitly, disjunctions on both integer and continuous variables.

Several solution approaches obtain a mixed-integer linear programming relaxation of the original problem, and rely on branch-and-cut techniques for solving the problem to global optimality. In the MINLP context, using disjunctions for branching has been subject to intense research, while the use of disjunctions as a means of generating valid linear inequalities has attracted some attention only recently.

We describe a straightforward extension of a separation method for disjunctive cuts that has shown to be very effective in Mixed-Integer Linear Programming (MILP). The theoretical and implementation aspects are very close to the MILP case, and, as the experimental results show, this extension obtains encouraging results in the MINLP case even when a simple separation method is used.