Show that the following problem is a convex optimization problem.
$f(x,y,z)=2x^2-y+z^2 \rightarrow min! $
Convex optimization problem if:
(1) $f(x)\rightarrow min!$
(2) $f(x)$ is convex
(3) all constraints $g_i$ are convex, $ i=1,..,m$
My idea is to calculate the Hessian matrix of the objective function and constraints and check if the matrix is positive (semi) definite, which would imply (strictly) convex function.
This is a positvie semidefinite matrix (Eigenvalues $\geq0$)
$\Rightarrow f(x)$ is convex
The Hessian matrix of $g_1$ and $g_2$ is a zero matrix which is both convex and concave.
So the problem is a convex optimization problem.
Is my computation/conclusion correct?
Thank you in advance.