# The Central Path

• Robert J. Vanderbei
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 114)

## Abstract

In this chapter, we begin our study of an alternative to the simplex method for solving linear programming problems. The algorithm we are going to introduce is called a path-following method. It belongs to a class of methods called interior-point methods. The path-following method seems to be the simplest and most natural of all the methods in this class, so in this book we focus primarily on it. Before we can introduce this method, we must define the path that appears in the name of the method. This path is called the central path and is the subject of this chapter. Before discussing the central path, we must lay some groundwork by analyzing a nonlinear problem, called the barrier problem, associated with the linear programming problem that we wish to solve.

## Keywords

Lagrange Multiplier Barrier Function Linear Programming Problem Central Path Nonempty Interior
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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