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Self-Dual Embedding Technique for Linear Optimization

  1. Kees Roos

Published Online: 15 FEB 2011

DOI: 10.1002/9780470400531.eorms0754

Wiley Encyclopedia of Operations Research and Management Science

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. .

Author Information

  1. Delft University of Technology, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft, The Netherlands

Publication History

  1. Published Online: 15 FEB 2011

Abstract

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.

Keywords:

  • linear optimization;
  • central path;
  • interior-point method;
  • optimal partition;
  • self-dual embedding