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Tighter upper bound for $\sum_{i=1}^kA_i\log(\frac{A_i}{e})$
What is the tightest upper bound one can obtain for the following expression
$$\sum_{i=1}^kA_i\log(\frac{A_i}{e})$$ subject to $\sum_{i = 1}^k A_i = C$ in terms of $C$ and $k$?
A very loose upper ...
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