An alternative method to solve a variational inequality applied to an air traffic control example

Some important problems of Air Traffic Control, such as collision avoidance, can mathematically be formulated as problems of optimal stopping a diffusion. As known, an optimal stopping policy can be characterized by a Variational Inequality (VI). To compute the solution of such a VI, a new iteration scheme is developed. The simplicity of this scheme is explicitly due to the assumption that the cost of stopping is a sufficiently smooth function of the state, which often holds for stopping problems. The scheme is applied to a simple example of Air Traffic Control.