Author | Klerk, Etienne de. author |
---|---|

Title | Aspects of Semidefinite Programming [electronic resource] : Interior Point Algorithms and Selected Applications / by Etienne de Klerk |

Imprint | Boston, MA : Springer US, 2002 |

Connect to | http://dx.doi.org/10.1007/b105286 |

Descript | XVI, 288 p. online resource |

SUMMARY

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 Lovรกsz 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

CONTENT

Theory and Algorithms -- Duality, Optimality, and Degeneracy -- The Central Path -- Self-Dual Embeddings -- The Primal Logarithmic Barrier Method -- Primal-Dual Affine-Scaling Methods -- Primal-Dual Path-Following Methods -- Primal-Dual Potential Reduction Methods -- Selected Applications -- Convex Quadratic Approximation -- The Lovรกsz ?-Function -- Graph Coulouring and the Max-K-Cut Problem -- The Stability Number of a Graph and Standard Quadratic Optimization -- The Satisfiability Problem

Computer science
Computer programming
Computers
Applied mathematics
Engineering mathematics
Computer mathematics
Algorithms
Mathematical optimization
Computer Science
Programming Techniques
Optimization
Applications of Mathematics
Algorithms
Theory of Computation
Computational Mathematics and Numerical Analysis