Algorithm for constraint partial inverse matroid problem with weight increase forbidden

In a partial inverse matroid problem, given a matroid M=(S,I)M=(S,I), a real valued weight function w on S  , and an independent set I0∈II0∈I, the goal is to modify the weight w   as small as possible to a new weight w¯ such that there exists a w¯-maximum base containing I0I0. In this paper, we study a constraint version of the partial inverse matroid problem in which the weight can only be decreased. A polynomial time algorithm is presented under l∞l∞-norm.