This is the first elementary exposition of the main ideas of complexity theory for convex optimization. Up to now, most of the material can be found only in special journals and research monographs. The book covers optimal methods and lower complexity bounds for smooth and non-smooth convex optimiza[...]
It was in the middle of the 1980s, when the seminal paper by Kar- markar opened a new epoch in nonlinear optimization. The importance of this paper, containing a new polynomial-time algorithm for linear op- timization problems, was not only in its complexity bound. At that time, the most surprising [...]