Extreme directions of a convex set

Dependencies:

1. Convex set
2. Direction of a convex set and Recession cone

Two vectors $u$ and $v$ are called collinear iff $v = \alpha u$ for some $\alpha > 0$.

Let $S$ be a convex set. Let $d$ be a non-zero direction of $S$. $d$ is said to be non-extreme for $S$ iff there exist non-zero non-collinear directions $x$ and $y$ of $S$ and $\exists \alpha > 0$, $\exists \beta > 0$ such that $d = \alpha x + \beta y$.

Dependency for:

1. Extreme direction of convex cone as extreme point of intersection with hyperplane
2. LP is optimized at BFS
3. Representing point in pointed polyhedral cone
4. Representing point in full-rank polyhedron

Info:

• Depth: 7
• Number of transitive dependencies: 8

Transitive dependencies:

1. Group
2. Ring
3. Field
4. Vector Space
5. Cone
6. Convex combination and convex hull
7. Convex set
8. Direction of a convex set and Recession cone