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.

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.

Reviewer: K.Schittkowski (Bayreuth)

##### MSC:

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 |