I am trying to solve the following problem in \Re^2:
\begin{eqnarray*}
&&\text{minimize}\ \ \ \ f_0(\textbf{x})=(x_1-3)^2+(x_2-2)^2\
&&\text{subject to}\ \ \ f_1(\textbf{x})=x_1^2+x_2^2-5\leq 0\
&&\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ f_2(\textbf{x})=-x_1\leq 0\
&&\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ f_3(\textbf{x})=-x_2\leq 0\
\end{eqnarray*}
where I want to find the primal optimal \textbf{x}^\ast=[x_1^\ast\ \ x_2^\ast]^T and the dual optimal, say \textbf{y}^\ast=[y_1^\ast\ \ y_2^\ast\ \ y_3^\ast]^T that satisfy the KKT conditions. I want to verify that the following CVX code is correct in order to solve the problem on my own and then check with CVX solution:
cvx_begin
variable x(2,1);
dual variables y1 y2 y3;
minimize ((x(1) - 3)^2 + (x(2) - 2)^2);
subject to
y1 : x(1)^2 + x(2)^2 - 5 <= 0;
y2 : -x(1) <= 0;
y3 : -x(2) <= 0;
cvx_end