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In Bertsimas' Introduction to Linear Optimization, we define the primal problem in standard form as minimizing $c'x$ subject to $Ax=b$ and $x\geq0$, and the dual problem as maximizing $p'b$ subject to $A^* p \geq c$.

He makes the comment that this definition of the dual problem requires $p_i$ to have the same sign as that of $a'_i x - b_i$. I've gone back through the derivation of the dual problem and its constraints a few time, and am having trouble understanding why this is.

Any thoughts?

Thanks!

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  • $\begingroup$ A good explanation about transforming a primal problem into a dual problem can be found here by Mike Spivey $\endgroup$ – callculus Mar 11 at 20:23

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