Self-Dual Embedding Technique for Linear Optimization
Published Online: 15 FEB 2011
Copyright © 2010 John Wiley & Sons, Inc. All rights reserved.
Wiley Encyclopedia of Operations Research and Management Science
How to Cite
Roos, K. 2011. Self-Dual Embedding Technique for Linear Optimization. Wiley Encyclopedia of Operations Research and Management Science. .
- Published Online: 15 FEB 2011
In the article titled Central Path and Barrier Algorithms for Linear Programs in this encyclopedia, the main ideas underlying the modern interior-point methods are presented. In these methods the central path plays a crucial role. To start these methods one needs a starting point on or close to the central path. Given such a point, a variant of Newton's method is used to generate a sequence of iterates that converges to an optimal solution of the problem. In this section, we show how to get into the situation that a starting point on the central path is known. This goes via the construction of an artificial problem whose solution either yields an optimal solution for a given problem, or detects that no such solution exists.
- linear optimization;
- central path;
- interior-point method;
- optimal partition;
- self-dual embedding