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Prove that any LP optimization problem can be transformed into the following form: \begin{align*} \text{minimize} && 0 · x \\ \text{subject to} && Ax &= b\\ && x&\ge 0 \end{align*}

If the LP is feasible, then it has an optimum value of 0

If the LP is not feasible, then it has an optimal value of infinity

0 is zero. I think the above function is not a dual function. How to prove it?

Zhiling Zheng
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  • How do you define LP-problem (so what form is your standard form)? And I doubt that that is true as written (because the function to minimize is a constant ... – martini Feb 08 '22 at 10:39
  • The standard form can be written as: maximize c^Tx with constraints Ax=b and x>=0. If we minimize or maximize a constant it's always true right? Because we have already had the optimal value which is that constant. – Zhiling Zheng Feb 08 '22 at 10:44

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