We are given a matroid. Our goal is to find a set of elements of minimum size that has non-empty intersection with every base of the matroid. Is the problem studied before? Is it in P? For example, in a spanning tree matroid, the minimum hitting set should be a minimum cut. Thanks.

Crossposted at [CSTheory](http://cstheory.stackexchange.com/questions/11498/min-hitting-set-of-every-base-of-a-matroid).