I am curious to know if all convex combinations are conic combinations? A convex combination is: $$C=\{x|x=\alpha_1x_1+...+\alpha_kx_k, \alpha_1+...+\alpha_k=1,\alpha_i\geq0\}$$ A conic combination is:$$C=\{x|x=\alpha_1x_1+...+\alpha_kx_k, \alpha_i\geq0\}$$
Is there an example of a convex combination that is not conic?
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$\begingroup$
convex-hulls
convex-cone
1 Answers
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There's hardly anything to be curious about when convex combination litterally has an additional condition compared to conic combination.