Applying Kuhn-Tucker theorem

• Jul 17th 2011, 04:00 AM
russel
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
$f(x,y,z)= \frac{1}{2}[(x-1)^{2}+(y-2)^{2}+(z-2)^{2}]$
under the constraints
$y=z$
$x^2+2y^2 \leq 1$
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...
• Jul 17th 2011, 02:49 PM
russel
Re: Applying Kuhn-Tucker theorem
Never mind, I found the solution: the trick is to use the first constraint $y=z$ and substitute it in the given function. Then, you get a new function $f(x,y)= \frac{1}{2}[(x-1)^{2}+2(y-2)^{2}]$ under only one constraint $x^{2}+2y^{2} \leq 1$
I hope it's correct!