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.

翻译：埃尔维斯问题在文献[2]中已有研究，该文献证明了解的存在性。然而，在非光滑情形下求解该问题仍未得到解决。本文针对二维空间中一般凸有界速度集，提出了一种二分法来求解埃尔维斯问题，并证明了其线性收敛速度。最后，通过对光滑和非光滑速度集进行数值实验，验证了该算法的稳健性。