# Finding simple min-weight path between two vertices in graph with negative edge weights

Given a weighted graph (negative weights are allowed) and two vertices $$u$$ and $$v$$, can we find the simple min-weight path between $$u$$ and $$v$$? There can be a negative cycle on the path from $$u$$ to $$v$$, but we want to ignore that, and calculate the weight of a simple path between them. Can this be done in polynomial time?