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Is there a geometric interpretation of the linear programming dual in terms of the primal? I feel like without some sort of intuition of it, I don't truly understand it.

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  • $\begingroup$ Here's a relevant thread, although it is not specific to linear programming. If there is special intuition that only applies to the LP case I'd be very interested to know about it. math.stackexchange.com/questions/223235/… $\endgroup$
    – littleO
    Jul 19, 2016 at 0:01
  • $\begingroup$ Do you know the general dual problem construction where you introduce the Lagrangian and then minimize with respect to the primal variables to obtain the dual function? Sometimes linear programming courses don't teach this. $\endgroup$
    – littleO
    Jul 19, 2016 at 0:03
  • $\begingroup$ @littleO Even knowing the general dual problem, it doesn't always hold much intuition without a geometric interpretation. $\endgroup$ Jul 19, 2016 at 0:06
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    $\begingroup$ Section 5.3 (p. 232) of Boyd and Vandenberghe gives a geometric interpretation of the dual problem that you might like. See figures 5.3, 5.4, 5.5, and 5.6. I think it's what you're looking for. The book is free online. Also, you might like the way Bertsekas explains it with his "min common / max crossing" viewpoint (which I think is very similar to what's in Boyd and Vandenberghe). $\endgroup$
    – littleO
    Jul 19, 2016 at 0:54
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    $\begingroup$ science4all.org/article/duality-in-linear-programming $\endgroup$
    – Kuifje
    Jul 23, 2016 at 19:40

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