How about *[Boosting](https://en.wikipedia.org/wiki/Boosting_(machine_learning))* and the *Hardcore Lemma*, as described in this paper?

> Trevisan, Luca, Madhur Tulsiani, and Salil Vadhan. "Regularity, boosting, and efficiently simulating every high-entropy distribution." *24th Annual IEEE Conference on Computational Complexity*, IEEE, 2009. ([PDF download](http://ttic.uchicago.edu/~madhurt/Papers/regularity-full.pdf).)

The *Hardcore Lemma* can be proved via LP duality:

> "if a problem is hard-on-average in a weak sense on uniformly distributed inputs, then there is a
'hardcore' subset of inputs of noticeable density
such that the problem is hard-on-average
in a much stronger sense on inputs randomly drawn from such set."