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Suppose $K$ is the closed convex hull generated by the canonical basis $\{e_n\}$ in $\mathcal{l}_2$. How do you find the unique closest to $0$ in $K$?

I don't have the foggiest idea about how to do that? Any references will be appreciated.

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Hint: What is the norm of $\dfrac{e_1+e_2+\cdots+e_n}{n}$?

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    Thank you very much, Jonas. It was really simple.2012-11-01