Maximum network flows with concave gains

This paper deals with a generalized maximum flow problem with concave gains, which is a nonlinear network optimization problem. Optimality conditions and an algorithm for this problem are presented. The optimality conditions are extended from the corresponding results for the linear gain case. The algorithm is based on the scaled piecewise linear approximation and on the fat path algorithm described by Goldberg, Plotkin and Tardos for linear gain cases. The proposed algorithm solves a problem with piecewise linear concave gains faster than the naive solution by adding parallel arcs. Supported by a Grant-in-Aid for Scientific Research (No. 13780351 and No.14380188) from The Ministry of Education, Culture, Sports, Science and Technology of Japan.