Find tangent cone to closed convex set
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Let $X = {xinmathbb{R}^5: x_i geq 0, x_1+2x_2-x_3 = 6,x_1 + x_2 + 2x_4 -x_5 = 4}$ , and I am looking to find the tangent cone to $X$ at the point $(0,4,2,0,0)$ . How would I go about this? I know that $X$ is closed and convex and therefore the tangent cone is just ${{a(y-(0,4,2,0,0)): y in X, a geq 0}}$ , but I think because it is in five dimensions I am having trouble picturing it. One idea I had was to find the normal cone, i.e. ${v in mathbb{R}^5: langle v, x-(0,4,2,0,0)rangle leq 0 forall x in X}$ , but I can't figure out how to do this either
calculus optimization convex-optimization
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edited Dec 10 '18 at 18...