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What are the fastest known algorithms for general convex optimisation under linear inequality constraints?

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That's a pretty wide question... –  Yuval Filmus Feb 11 '13 at 15:40
    
In which direction would you like to see it narrowed? –  alang Feb 11 '13 at 23:58
    
It shouldn't necessarily be narrowed - but the answer should be a mini-survey. –  Yuval Filmus Feb 12 '13 at 5:26
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