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.
Citation
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).