# The Homogeneous Self-Dual Method

• Robert J. Vanderbei
Chapter
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 196)

## Abstract

In Chapter 18, we described and analyzed an interior-point method called the path-following algorithm. This algorithm is essentially what one implements in practice but as we saw in the section on convergence analysis, it is not easy (and perhaps not possible) to give a complete proof that the method converges to an optimal solution. If convergence were completely established, the question would still remain as to how fast is the convergence. In this chapter, we shall present a similar algorithm for which a complete convergence analysis can be given.

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