Inverse Maximum Flow Problem Under the Combination of the Weighted l _2 Norm and the Weighted Hamming Distance

The idea of the inverse optimization problem is to adjust the values of the parameters so that the observed feasible solutions are indeed optimal. The modification cost is measured by different norms, such as l_1, l_2, l_∞ norms and the Hamming distance, and the goal is to adjust the parameters as little as possible. In this paper, we consider the inverse maximum flow problem under the combination of the weighted l_2 norm and the weighted Hamming distance, i.e., the modification cost is fixed in a given interval and depends on the modification out of the given interval. We present a combinatorial algorithm which can be finished in O ( nm ) to solve it due to the minimum cut of the residual network.