Faces should be implemented on PointedCone. Some theory might already exist on ConvexCone but might look different from what we want.
We should use the definition of faces as an extremal set (if for any two points $$x,y \in C$$ their conic span intersects the face $$F$$, then $$x,y\in F$$). Later we define "exposed face" as the intersection with a supporting hyperplane. This notion is weaker, but is the same on polyhedral cones, as we need to show.
Faces should be implemented on
PointedCone. Some theory might already exist onConvexConebut might look different from what we want.We should use the definition of faces as an extremal set (if for any two points$$x,y \in C$$ their conic span intersects the face $$F$$ , then $$x,y\in F$$ ). Later we define "exposed face" as the intersection with a supporting hyperplane. This notion is weaker, but is the same on polyhedral cones, as we need to show.