minimize $\sum_{i=1}^{k}\alpha_{i}^{2}$ subject to $\sum_{i=1}^{k}\alpha_{i}=0$ and $\max_{1\leq i<j\leq k}|\alpha_{i}-\alpha_{j}|\geq \delta$. I think the solution is $\alpha_{i} = -\frac{\delta}{2}$, $\alpha_{j} = \frac{\delta}{2}$ and $\alpha_{l} = 0$ for all $l\neq i, j$. I need to prove. Thanks
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You are on the right track but note that the minimum distance constraint must hold for any pair. – mlc May 25 '17 at 09:53
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Whether $k$ is odd or even has some relevance to the exact specification of the solution. – mlc May 25 '17 at 09:55