Given two convex polygons $P$ and $Q$ what is the minimum intersection polygon $A=P\cap Q'$ where $Q'$ is the polygon $Q$ offset by a vector $\overline r$ of fixed length?
Put another way, what is the vector $\overline r_{min}$ that minimizes $P\cap (Q+\overline r)$? Is there an algoritm that finds this "direction of minimum overlap"? Does this problem has a name?
