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Elad Hazan
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Why introduce a new algorithm when you can reduce the number of algorithms? 

Ladies and Gentlemen: one less algorithm to study in "advanced algorithms"/"convex optimization":
Together with my good friend magician-turned-machine-learner Jacob Abernethy we have discovered that the two most common poly-time convex optimization algorithms are very much related: 
The yellow line in the picture is the central path of interior point methods (with the entropic barrier function). The big squares are the means of the simulated annealing algorithm (what we dub the "heat path"). et voila - they are the same!
For a full proof see http://arxiv.org/abs/1507.02528 (& we'll throw in a faster convex optimization algorithm for free).
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