Fast convergence of the simplified largest step path following algorithm

Each master iteration of a simplified Newton algorithm for solving a system of equations starts by computing the Jacobian matrix and then uses this matrix in the computation of p Newton steps: the first of these steps is exact, and the others are called ‘simplified’. In this paper we apply this approach to a large step path following algorithm for monotone linear complementarity problems. The resulting method generates sequences of objective values (duality gaps) that converge to zero with Q-order p + 1 in the number of master iterations, and with a complexity of O(√(n)L) iterations.