Before revision: While there are well-developed tools for maximizing a  submodular function subject to a matroid constraint , there is much less work on the corresponding supermodular maximization problems. We develop new techniques for attacking these problemsinspired by the continuous greedy method{2}i,j\in AA_{ij}:S\inM, where M is a matroid.
After revision: While there are well-developed tools for maximizing a submodular function subject to a matroid constraint . This framework has a continuous optimization part and a rounding part. We extend both parts to a wider array of problems. In particular, we make a conceptual contribution by identifying a family of parameterized functions. As a running example we focus on solving diversity problems \max f(S)=\frac{1{2}i,j\in AA_{ij}:S\inM, where M is a matroid.