Interior Point Algorithms For Linear Complementarity Problems Based On Large Neighborhoods Of The Central Path

In this paper we study a rst-order and a high-order algorithm for solving linear complementarity problems. These algorithms are implicitly associated with a large neighborhood whose size may depend on the dimension of the problems. The complexity of these algorithms depends on the size of the neighborhood. For the rst order algorithm, we achieve the complexity bound which the typical large-step algorithms possess. It is well-known that the complexity of large-step algorithms is greater than that of short-step ones. By using high-order power series (hence the name high-order algorithm), the iteration complexity can be reduced. We show that the complexity upper bound for our high-order algorithms is equal to that for short-step algorithms.