Given the following problem \begin{align}\min&\quad x_1+2x_2+3x_3+4x_4+\sum_{i=1}^4x_i\ln(x_i)\\\text{s.t.}&\quad e^\top x=1\\&\quad x\geq0\end{align}
I was asked to solved the dual problem and I think I've managed to do so, I've got $$q(\lambda)=-e^{-\lambda}(e^{-2}+e^{-3}+e^{-4}+e^{-5})-\lambda.$$ I wanted to check if I'm right so I wanted to check with CVX via matlab but the following code doesn't work.
cvx_begin
variable x(4)
minimize (x(1)+2*x(2)+3*x(3)+4*x(4)+x(1)*log(x(1))+x(2)*log(x(2))+x(3)*log(x(3))+x(4)*log(x(4)))
sum(x)==1
x>=0
How can I fix the objective function? (I know the problem is at $x_i\ln(x_i)$)