# hardness of approximation result for a Min-CSP, by reduction from PCPs

Reduction from PCPs allow us to prove hardness of approximation results for a number of constraint satisfaction problems. I've seen such a reductions only for Max-CSPs. Is this possible only for Max-CSPs? In other words, can someone get hardness of approximation result for a Min-CSP (for example, Vertex-Cover or sparsest-cut) by reduction from PCPs?

If it is always possible to convert a Min-CSP to an equivalent Max-CSP, then maybe this answers my question. But, I don’t know whether it is always possible or not.