Is there a somewhat intuitive way of understanding strong duality in linear programming? I do understand weak duality quite well since it pretty much follows from how the dual problem is defined but I don't understand why strong duality holds. I even looked up a proof of strong duality and studied every step of the proof very carefully and rewrote the proof on my own in an attempt understand just why it holds but it is still mysterious to me. I'm not necessarily looking for geometric intuition since that's probably quite tricky, but I would like some ideas as to why one might expect strong duality to hold for linear programming. I know similar questions have been asked on here about more general duality problems, but I want to focus on linear programming until I deal with more advanced topics.
2026-03-25 17:26:31.1774459591
Can strong duality for linear programming be viewed intuitively?
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