Interior Point Polynomial Methods in Convex Programming

In this book, the authors describe the first unified theory of polynomial-time interior-point methods.

Yurii Nesterov (Author), Arkadii Nemirovskii (Author)

9780898715156, Society for Industrial and Applied Mathematics

Paperback / softback, published 30 June 2006

414 pages
22.9 x 15.2 x 2 cm, 0.728 kg

Written for specialists working in optimization, mathematical programming, or control theory. The general theory of path-following and potential reduction interior point polynomial time methods, interior point methods, interior point methods for linear and quadratic programming, polynomial time methods for nonlinear convex programming, efficient computation methods for control problems and variational inequalities, and acceleration of path-following methods are covered. In this book, the authors 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; this approach yields polynomial-time interior-point methods for a wide variety of problems beyond the traditional linear and quadratic programs.

1. Self-concordant functions and Newton method
2. Path-following interior-point methods
3. Potential Reduction interior-point methods
4. How to construct self- concordant barriers
5. Applications in convex optimization
6.Variational inequalities with monotone operators
7. Acceleration for linear and linearly constrained quadratic problems
Bibliography
Appendix 1
Appendix 2.

Subject Areas: Miscellaneous items [WZ]