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, the algorithm is further applied to robust design of the magnetic shielding.
Research Memorandum No. 775, The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106-8569 Japan, October, 2000 (Final revision: September 2002) (To appear in SIAM Journal on Scientific Computing).