A Bisection Method to Solve The Elvis Problem With Convex Bounded Velocity Sets

The Elvis problem has been studied in [2], which proves existence of solutions. However, their computation in the non-smooth case remains unsolved. A bisection method is proposed to solve the Elvis problem in two space dimensions for general convex bounded velocity sets. The convergence rate is proved to be linear. Finally, numerical tests are performed on smooth and non-smooth velocity sets demonstrating the robustness of the algorithm.