Optimal magnetic shield design with second-order cone programming

In this paper, we consider a continuous version of the convex network flow problem which involves the integral of the Euclidean norm of the flow and its square in the objective function. A discretized version of this problem can be cast as a second-order cone program, for which efficient primal-dual interior-point algorithms have been developed recently. An optimal magnetic shielding design problem of the MAGLEV train, a new bullet train under development in Japan, is formulated as the continuous convex network flow problem and is solved with the primal-dual interior-point algorithm. Taking advantage of its efficiency and stability, we further apply the algorithm to robust design of the magnetic shielding.