I have an optimization problem which I would like to know whether it is linear or convex.
There are three variables $x_0$, $x_1$ and $x_2$ for which the optimization problem should be minimized.
Constraint: $\sum_{i=0}^{3}x_n = 1$
Boundaries: $0 \leq x_n \leq 1$
Objective: $Minimize\ \ \ || \pmb{v_3} - (x_0\pmb{v_0} + x_1\pmb{v_1} + x_2\pmb{v_2}) ||$
where $x_0$, $x_1$ and $x_2$ are scalars and $\pmb{v_0}$, $\pmb{v_1}$, $\pmb{v_2}$ and $\pmb{v_3}$ vectors of the same size.
Is my optimization problem linear or convex? And why?