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What is the minimum for this function of $x_1,x_2, \ldots, x_n$:

$$\sum_{i=1}^n c_i \log x_i + \lambda \; \sum_{i=1}^n d_i x_i, $$ where $\lambda$, $c$ and $d$ series are positive constants, $x_i \in (0.02,1]$ and $\sum x_i = 1$.

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    how about letting any $x_i \to 0$, then your function goes to $-\infty$, so it does not have a minimum (assuming that the corresponding $c_i > 0$.2010-11-06
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    Forgot to add.. $x_i \epsilon (0,1]$2010-11-06
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    A minimum, many minima.2010-11-06
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    Another way of saying Slowsolver's comment: you have a ceiling, but certainly no floor.2010-11-06
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    Right. its a concave function and so the minima is $-\infty$. I am thinking about adding some bounds and constraints. Something like $x_i \epsilon (0.02,1]$ and $\sum x_i = 1$.2010-11-06
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    For the "in" operator, use `\in`, not `\epsilon`. (Also what's up with the ugly sans-serif math font, did I miss something?)2011-01-05

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