A full-Newton step interior-point algorithm based on modified Newton direction

摘要

The central path plays a very important role in interior-point methods. By an equivalent reformulation of the central path, we obtain a new search direction which targets at a small neighborhood of the central path. For a full-Newton step interior-point algorithm based on this search direction, the complexity bound of the algorithm is the best known for linear optimization. Highlights: The central path plays a very important role in interior-point methods. By an equivalent reformulation of the central path, we obtain a new search direction. The new direction targets a small neighborhood of the central path. Based on this search direction, we present a full-Newton step interior-point algorithm. The complexity bound of the algorithm is the best known for linear optimization.