How to maximize $\sum_i^n\dfrac{1}{2^{v_i}}$ where $, v_i\in \mathbb{N}$, $0\leq v_i<k$ and $\sum_i^n\dfrac{1}{2^{v_i}}\leq 1$?. Could you give an idea to start to find an equivalent problem only using integer constraints?
Consider $n,k$ constants
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What are you optimizing on? $n$, $k$, or $v$? – nejimban Sep 12 '21 at 08:59
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@nejimban on v. $k$ and $n$ are constants – juaninf Sep 12 '21 at 09:02
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1Then I think $v_1=v_2=\ldots=v_n=1$ give the maximum. – nejimban Sep 12 '21 at 09:10
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@nejimban in this case the constraint $\sum_i2^{-v_i}\leq1$ is not satisfied for $n>2$. – leoli1 Sep 12 '21 at 10:47
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@leoli Indeed, I missed that… What about $v_i=i$ if $1\le i<k$, and $v_i=0$ otherwise? – nejimban Sep 12 '21 at 13:32