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### convex-concave function

Inviato: 03 gen 2018, 15:49
How do you prove that if $f(x)$ is a convex-concave function, $\min\left(\sum_{i=1}^nf\left(x_i\right)\right)$ is when $x_1=x_2=...=x_n$ wher $x_i \in$ convex part of $f$ or when $x_1 \neq x_2=x_3=...=x_n$ wher $x_1 \in$ concave part of $f$ and $x_i \in$ convex part of $f$ (for $i >1$ ) ?