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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.

Daishisan
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  • 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. http://math.stackexchange.com/questions/223235/please-explain-the-intuition-behind-the-dual-problem-in-optimization – littleO Jul 19 '16 at 00:01
  • 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. – littleO Jul 19 '16 at 00:03
  • @littleO Even knowing the general dual problem, it doesn't always hold much intuition without a geometric interpretation. – Christopher A. Wong Jul 19 '16 at 00:06
  • @ChristopherA.Wong I agree, absolutely (see the question I linked to, for example). But still, learning the general dual problem construction is a big step forward from just memorizing the dual of a linear program, as is done in some linear programming courses. – littleO Jul 19 '16 at 00:14
  • @littleO I've heard such justifications of the dual, but I was hoping that the dual would have a geometric interpretation as that's generally best for my intuition. Also my understanding of convex optimization if tentative at best unfortunately, so I'm having a somewhat hard time reading the linked math.stackexchange post. Nonetheless, thanks for the reference! – Daishisan Jul 19 '16 at 00:33
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    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). – littleO Jul 19 '16 at 00:54
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    http://www.science4all.org/article/duality-in-linear-programming/ – Kuifje Jul 23 '16 at 19:40
  • I found this useful: https://www.coursera.org/lecture/approximation-algorithms-part-2/geometry-of-lp-duality-Zjfj2 – Geordie Williamson Sep 11 '18 at 00:55

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