Perspective Reformulations-based Strengthening for the Sequential Convex MINLP Technique

The Sequential Convex MINLP (SC-MINLP) technique is a global optimization algorithm aimed at solving NonConvex Mixed-Integer NonLinear Problems with separable nonconvexities. At each iteration, it provides a lower and an upper bound by solving a Convex MINLP and a NonConvex NLP, respectively. The convex MINLPs are iteratively improved by adding breakpoints to the linearization of the concave parts of the problem. We propose to strengthen the convex MINLPs by exploiting its structure and modifying the convex terms using the Perspective Reformulation technique to strengthen the bounds. Experimental results on different classes of instances show a significant decrease of the solution time of the Convex MINLPs, i.e., the most time-consuming part of SC-MINLP, and has, therefore the potential to improving its overall effectiveness.