Complex number formulation and convex relaxations for aircraft conflict resolution

We present a novel complex number formulation along with tight convex relaxations for the aircraft conflict resolution problem. Our approach combines both speed and heading control and provides global optimality guarantees despite non-convexities in the feasible region. We present a new characterization of the conflict separation condition in the form of disjunctive linear constraints. Using our approach, we are able to close a number of open instances and reduce computational time by up to two orders of magnitude on standard instances.