For an exam I have to prove that if a constrained problem has no duality gap for some $(l,g)$ and $x$, then $x$ is a global minimum point for the constrained problem. Do you think an example is sufficient?
2026-03-28 13:59:21.1774706361
Prove constrained problem has no duality gap
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No, example would not be sufficient for a general proof. Just because this is true for your example, does not mean it is generally true.