I would like to minimize the following function:
$f(x)=log(e^{-x_1}+..+e^{-x_n})$
Subject to:
$\sum_{i=1}^{n}{x_i}=1$
$0 \leq x_i \leq 1$
So far I have discovered the following: If all the $x_i$'s are equal, $f(x)=max(x_i)+log(n)$, but I have not been able to find a conclusive answer regarding what would be the value of the $x_i$'s for the minimum value of the function.