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Math Help - Applying Kuhn-Tucker theorem

  1. #1
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    Athens, Greece
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    Question 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...
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  2. #2
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    Sep 2009
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    Athens, Greece
    Posts
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    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!
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