Studying Nesterov's Smoothing Technique

Background and Description

Among first-order nonlinear optimization, there is a significant gap between the best methods for smooth and nonsmooth objective functions. Although these methods are "provably optimal", that does not necessarily mean that we cannot do any better. Nesterov's smoothing technique proposes the idea that rather than directly minimize a nonsmooth function, we can instead approximate it by a smooth one and minimize the approximation instead. This is a brief summary of the approach.