In this book, Nesterov and Nemirovskii describe the first unified theory of
polynomial-time interior-point methods. Their approach provides a simple and
elegant framework in which all known polynomial-time interior-point methods
can be explained and analyzed. Perhaps more important for applications, their
approach yields polynomial-time interior-point methods for a very wide variety
of problems beyond the traditional linear and quadratic programs.
The book contains new and important results in the general theory of convex
programming, e.g., their "conic" problem formulation in which duality
theory is completely symmetric. For each algorithm described, the authors
carefully derive precise bounds on the computational effort required to solve
a given family of problems to a given precision. In several cases they obtain
better problem complexity estimates than were previously known