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According to the Wikipedia article, the Simplex algorithm depends on constraining all the unknowns to be >= 0. I have a problem where one of my variables is highly likely to be negative in many cases. How can I adapt the problem so I can use Simplex?

EDIT: example: say I have x, y and z and I want to find values (both >= 0) for x and y which minimize z, where I also have the constraints:

1.4x -y +z >= 0 -x +2.2y +z >= 0 
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    I don't see the problem. I mean, if you think there might be a negative solution, switch the sign of one variable everywhere in the problem. Solve it (maximize for z of course) and switch back.2011-03-03

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The standard trick is to replace $z$ with $z^+ - z^-$ throughout.

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    ...with $z^+$ and $z^-$ both taken to be nonnegative.2011-03-04