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As per Lagrange theorem it says I can get maximum or minimum under some constraint.
Example:

$f(x,y)=x^2+y^2+4$ under constraint $x+y=2$. I can use Lagrange theorem for this.

But I have a problem like $f(x,y)=x^2+y^2+4$ under constraint like $x$ should be minimum.

How can I solve this any theorem or solution?

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    Is the equation $2x$ or $x^2$?2012-10-14
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    x(square) I just showed example.I am interested in knowing which theorem to solve this?2012-10-14
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    What do you mean by saying "$x$ should be minimum"? If you're optimizing both $f$ and $x$, you have to say something about the relative importance of these objectives; otherwise the problem isn't fully defined. See also http://en.wikipedia.org/wiki/Multi-objective_optimization.2012-10-14
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    What do you mean by $x$ should be minimum?2012-10-14
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    I have real time problem in technology .I am trying to get best equation to solve it.The constraint can be ambiguous like x can be minimum and x can be maximum or y is minimum and y is maximum2012-10-14
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    When you say the constraint can be ambiguous, that normally poses some sort of problem. In your problem, you can make $x$ as "minimal" as you want by taking $x\rightarrow -\infty$. But what exactly are you trying to accomplish?2012-10-14
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    @EuYu: I assume the OP is just trying to give an example. A better statement might be "Minimize $f$ under the constraint $g$ is also minimized."2013-05-15

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