Is this function strictly convex and why?

Question

Is this function strictly convex?

$(x_1+x_2+x_3+x_4+x_5+x_6-30)^2+(x_7+x_8+x_9+x_{10}+x_{11}-24)^2+(x_1+x_7+x_8+x_4-14)^2$

variables are $x_i$ and we have $1 \le x_i \le 9$.

Answer 1

Hint: fix all variables but $x_2$ and $x_3$ and have a look at the two-dimensional function (depending only on $x_2$ and $x_3$.

Note that a sum of squares is not always strictly convex, i.e., $(x_1,x_2) \mapsto x_1^2$.