How can i prove $f(x_1,\ldots,x_n) = \sum x_i\ln x_i - (\sum x_i )\ln(\sum x_i)$ is convex on R++
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1Please reproduce your question within the body of the question. There are many reasons this is a good practice, but for one example note that LaTeX isn't rendered properly in titles on the android app. – Matt Samuel May 14 '15 at 12:49
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1Can you add what you have tried? – wythagoras May 14 '15 at 13:03
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1I am thinking it has something to do with the Jensen inequality, – yonigo May 14 '15 at 13:07
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1Try taking partial derivatives and prove $\left(\frac{\partial^2 f }{\partial x_i \partial x_j}\right)$ is symmetric and positive semi-definite. – Michael May 14 '15 at 13:37
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How odd that this was posted twice in one day. http://math.stackexchange.com/questions/1281612/convexity-proof-of-a-function-including-ln-and-sums#comment2602514_1281612 – Michael Grant May 14 '15 at 19:07
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I'm voting to close this question as off-topic because it is a duplicate. – quid May 14 '15 at 23:27
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@quid: The other question now has an answer, so I closed this for being a duplicate. – robjohn May 16 '15 at 18:32