Abstract:

Mixed-Integer Nonlinear Programming (MINLP) is the problem of minimizing a non-linear function subject to non-linear constraints and to integrality of a subset of the variables. MINLP problems are ubiquitous: Engineering, Computational Biology, and Portfolio Optimization are just a few fields of application. Non-convex MINLPs are the most general class of MINLP problems, as they comprise bilinear, polynomial, and trigonometric objective functions and constraints.

As part of a joint research project between IBM and Carnegie Mellon University, we have developed Couenne, a spatial branch&bound solver for non-convex MINLPs. Couenne is an Open Source solver available in the Coin-OR framework (www.coin-or.org); it implements techniques for linearization, bound reduction, branching, and for obtaining feasible solutions. We present the main features of Couenne and discuss some computational experiments on publicly available MINLP instances.