  In minimum-cost inverse optimization problems, we are given a feasible
solution to an underlying optimization problem together with a linear cost
function, and the goal is to modify the costs by a small deviation vector so
that the input solution becomes optimal.
  The difference between the new and the original cost functions can be
measured in several ways. In this paper, we focus on two objectives: the
weighted bottleneck Hamming distance and the weighted $\ell_\infty$-norm. We
consider a general model in which the coordinates of the deviation vector are
required to fall within given lower and upper bounds. For the weighted
bottleneck Hamming distance objective, we present a simple, purely
combinatorial algorithm that determines an optimal deviation vector in strongly
polynomial time. For the weighted $\ell_\infty$-norm objective, we give a
min-max characterization for the optimal solution, and provide a
pseudo-polynomial algorithm for finding an optimal deviation vector that runs
in strongly polynomial time in the case of unit weights. For both objectives,
we assume that an algorithm with the same time complexity for solving the
underlying combinatorial optimization problem is available.
  For both objectives, we also show how to extend the results to inverse
optimization problems with multiple cost functions.
