Inverse constrained bottleneck problems under weighted l∞l∞ norm

In this paper, we consider a class of inverse constrained bottleneck problems (ICBP). Given two weight vectors w1w1 and w2w2, the constrained bottleneck problem is to find a solution that minimizes w1w1-bottleneck weight subject to a bound constraint on w2w2-sum weight. In its inverse problem (ICBP), however, a candidate solution is given, and we wish to modify the two weight vectors under bound restrictions so that the given solution becomes an optimal one to the constrained bottleneck problem and the deviation of the weights under weighted l∞l∞ norm is minimum. When the modifications of the two weight vectors are proportional, we present a general method to solve the problem (ICBP) and give several examples to implement the method including the inverse constrained bottleneck spanning tree problem and the inverse constrained bottleneck assignment problem.