Central Path and Barrier Algorithms for Linear Optimization
Published Online: 14 JAN 2011
Copyright © 2010 John Wiley & Sons, Inc. All rights reserved.
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. .
- Published Online: 14 JAN 2011
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.
- linear optimization;
- central path;
- interior-point method;
- barrier function;
- primal method;
- primal–dual method;
- dual method;
- KKT condition;