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For questions involving the concept of convexity
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Linearly independent support vectors of a convex set
Let $\Omega\subset\mathbb{R}^n$ a compact strictly convex set containing $0$ in its interior and let $k\leq n$.
Given a vector $x\neq 0$ in $\mathbb{R}^n$ a supporting vector $\xi_x$ in the directio …