Inverse optimization with multiple weights

In a recent paper titled Inverse optimization problems with multiple weight functions, we introduce a new class of inverse optimization problems in which an input solution is given together with k linear weight functions, and the goal is to modify the weights by the same deviation vector p so that the input solution becomes optimal with respect to each of them, while minimizing the 1-norm of p. In particular, we concentrate on three problems with multiple weight functions: the inverse shortest st path, the inverse bipartite perfect matching, and the inverse arborescence problems. Unlike in the case of a single weight function, the optimal p is not necessarily integral even when the weight functions are so, therefore computing an optimal solution becomes more difficult.