Central Region Method

In this chapter, we discuss a modification of the standard path-following scheme that tends to speed up the global convergence. This modification, the central region method, generates iterates that do not really trace the central path, or at least not closely. In this way, it has a relatively large freedom of movement, and consequently the ability to take long steps. This makes it interesting to consider more sophisticated search directions. We propose a search direction that is built up in three phases, viz. 1. Initial centering, 2. Predictor, 3. Second order centrality corrector.