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Central Path and Barrier Algorithms for Linear Optimization

  1. Kees Roos

Published Online: 14 JAN 2011

DOI: 10.1002/9780470400531.eorms0138

Wiley Encyclopedia of Operations Research and Management Science

Wiley Encyclopedia of Operations Research and Management Science

How to Cite

Roos, K. 2011. Central Path and Barrier Algorithms 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: 14 JAN 2011

Abstract

In this article, the main ideas underlying the modern interior-point methods are presented. We discuss primal, dual, and primal-dual methods and show that each of these methods can be used to solve a linear optimization problem in polynomial time. It is made clear that the central path plays a crucial role in each of the methods. The described methods require a starting point on or close to the central path. Given such a point, a variant of Newton's method can be used to construct a numerical procedure that generates a sequence of iterates that converges to an optimal solution of the problem.

Keywords:

  • linear optimization;
  • central path;
  • interior-point method;
  • barrier function;
  • primal method;
  • primal–dual method;
  • dual method;
  • KKT condition;
  • complexity