Applying Kuhn-Tucker theorem

Hello to everybody. I'm totally desparate about a problem I'm trying to solve and can't. Could anybody help me?

I want to **minimize** the quadratic function

$\displaystyle f(x,y,z)= \frac{1}{2}[(x-1)^{2}+(y-2)^{2}+(z-2)^{2}]$

under the constraints

$\displaystyle y=z$

$\displaystyle x^2+2y^2 \leq 1$

using the Kuhn-Tucker theorem... I'm troubled when I find a value of y that must be equal to z and I can't find the minimum...

Re: Applying Kuhn-Tucker theorem

Never mind, I found the solution: the trick is to use the first constraint $\displaystyle y=z$ and substitute it in the given function. Then, you get a new function $\displaystyle f(x,y)= \frac{1}{2}[(x-1)^{2}+2(y-2)^{2}]$ under only one constraint $\displaystyle x^{2}+2y^{2} \leq 1$

I hope it's correct!