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    Functions: K-T Condition

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    Consider the following program:

    Maximize f(x,y)=x^2+4xy+y^2
    subject to g(x,y)=x^2+y^2-1=0

    © BrainMass Inc. brainmass.com October 9, 2019, 3:35 pm ad1c9bdddf
    https://brainmass.com/math/graphs-and-functions/functions-kuhn-tucker-condition-7945

    Solution Preview

    Solution. Let us denote the gradient vector of the function f(x,y) by Df(x,y). We rewrite the original program as follows.
    Minimize F(x,y)=-f(x,y)=-x^2-4xy-y^2
    . g(x,y)=x^2+y^2-1=0.
    Since DF(x,y)=(-2x-4y,-4x-2y)', Dg(x,y)=(2x,2y)', by K-T ...

    Solution Summary

    A function is maximized using Kuhn-Tucker condition. The maximized function results are determined.

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