OUTER APPROXIMATION METHOD FOR THE MINIMUM MAXIMAL FLOW PROBLEM

The minimum maximal flow problem is the problem of minimizing the flow value on the set of maximal flows of a given network. The optimal value indicates how inefficiently the network can be utilized in the presence of some uncontrollability. After extending the gap function characterizing the set of maximal flows, we reformulate the problem as a D.C. optimization problem, and then propose an outer approximation algorithm. The algorithm, based on the idea of ε-optimal solution and local search technique, terminates after finitely many iterations with the optimal value of the problem.