Primal-dual interior-point methods. (English) Zbl 0863.65031

Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics. xx, 289 p. (1997).
The goal of the book is to summarize the present state-of-the-art of primal dual interior-point methods for linear programming. The book is organized as follows:
1. Introduction. 2. Background: Linear programming and interior-point methods. 3. Complexity theory. 4. Potential-reduction methods. 5. Path-following algorithms. 6. Infeasible-interior-point algorithms. 7. Superlinear convergence and finite termination. 8. Extensions. 9. Detecting infeasibility. 10. Practical aspects of primal-dual algorithms. 11. Implementations. 12. Basic concepts and results. 13. Software packages.
The main emphasis is to provide the analysis required to understand the basic methodology and the mathematical algorithms that are in practical use today. Some information about numerical implementation and available software is given. The book consists of 289 pages and contains 164 references.
It is a pleasure to read the book. The presentation of basic analysis, algorithms and convergence results is very clear and complete. The book is up-to-date and very useful for own research activities in the area. On the other hand it can be recommended also for newcomers and for usage as a textbook for courses on linear programming.


65K05 Numerical mathematical programming methods
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
90-02 Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming
90-04 Software, source code, etc. for problems pertaining to operations research and mathematical programming
90C05 Linear programming
90C51 Interior-point methods
90C06 Large-scale problems in mathematical programming