I recently came across the following problem: Let $ K \subseteq \mathbb{R}^2 $ be a closed convex cone (meaning K is closed under non negative linear combinations) and I am asked to show it is polyhedral meaning it is the intersection of finitely many half spaces, or alternatively that it is finitely generated $ K […]

Given a closed convex cone $D$ in $\mathbb{R}^{n}$, the cone $K_{2} \in \mathbb{R}^{m}$ is defined by $$ K_{2} = \{ y = (y^{1}, y^{2}, \cdots , y^{m}): y^{i} \in \mathbb{R}^{n},\, i= 1, \cdots , m, \, y^{1} + y^{2} + \cdots + y^{m} \in D \} $$ I need to describe its polar cone $K_{2}^{\circ}$. […]

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