Topics In Semidefinite And Interior Point Methods
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Topics in Semidefinite and Interior-Point Methods
Author: Panos M. Pardalos and Henry Wolkowicz
language: en
Publisher: American Mathematical Soc.
Release Date: 1998
Contains papers presented at a workshop held at The Fields Institute in May 1996. Papers are arranged in sections on theory, applications, and algorithms. Specific topics include testing the feasibility of semidefinite programs, semidefinite programming and graph equipartition, the totally nonnegative completion problem, approximation clustering, and cutting plane algorithms for semidefinite relaxations. For graduate students and researchers in mathematics, computer science, engineering, and operations. No index. Annotation copyrighted by Book News, Inc., Portland, OR
Aspects of Semidefinite Programming
Author: E. de Klerk
language: en
Publisher: Springer Science & Business Media
Release Date: 2002-03-31
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.
Low-Rank Semidefinite Programming
Finding low-rank solutions of semidefinite programs is important in many applications. For example, semidefinite programs that arise as relaxations of polynomial optimization problems are exact relaxations when the semidefinite program has a rank-1 solution. Unfortunately, computing a minimum-rank solution of a semidefinite program is an NP-hard problem. This monograph reviews the theory of low-rank semidefinite programming, presenting theorems that guarantee the existence of a low-rank solution, heuristics for computing low-rank solutions, and algorithms for finding low-rank approximate solutions. It then presents applications of the theory to trust-region problems and signal processing.