Introductory Lectures on Convex Optimization

It was in the middle of the 1980s, when the seminal paper by Kar­ markar opened a new epoch in nonlinear optimization. Approximately at that time the author was asked to prepare a new course on nonlinear optimization for graduate students. This is an elementary exposition of the main ideas of complexity theory for convex optimization. The book covers optimal methods and lower complexity bounds for smooth and non-smooth convex optimization. A separate chapter is devoted to polynomial-time interior-point methods.