Ebook: Aspects of Semidefinite Programming: Interior Point Algorithms and Selected Applications
Author: Etienne de Klerk (auth.)
- Genre: Computers // Programming
- Tags: Optimization, Algorithms, Theory of Computation, Computational Mathematics and Numerical Analysis, Combinatorics
- Series: Applied Optimization 65
- Year: 2004
- Publisher: Springer US
- City: Dordrecht; Boston
- Edition: 1
- Language: English
- djvu
Semidefinite programming has been described as linear programming for the year 2000. It is an exciting new branch of mathematical programming, due to important applications in control theory, combinatorial optimization and other fields. Moreover, the successful interior point algorithms for linear programming can be extended to semidefinite programming.
In this monograph the basic theory of interior point algorithms is explained. This includes the latest results on the properties of the central path as well as the analysis of the most important classes of algorithms. Several "classic" applications of semidefinite programming are also described in detail. These include the Lovász theta function and the MAX-CUT approximation algorithm by Goemans and Williamson.
Audience: Researchers or graduate students in optimization or related fields, who wish to learn more about the theory and applications of semidefinite programming.
This monograph has grown from my PhD thesis Interior point Methods for Semidefinite Programming [39] which was published in December 1997. Since that time, Semidefinite Programming (SDP) has remained a popular research topic and the associated body of literature has grown considerably. As SDP has proved such a useful tool in many applications, like systems and control theory and combinatorial optimization, there is a growing number of people who would like to learn more about this field.