Dual cone

Summary

The dual cone of a set $C$ in $\R^n$ is the set of vectors that make a nonnegative dot product with every vector of $C$. It is always a closed convex cone, and for a closed convex cone $C$ the dual of the dual is $C$ again. Dual cones are the geometric side of duality in linear and conic optimisation, and they appear in Farkas-type theorems of the alternative.