The Mizuno-Todd-Ye algorithm in a larger neighborhood of the central path

The Mizuno–Todd–Ye predictor–corrector method based on two neighborhoods DðaÞ DðaÞ of the central path of a monotone homogeneous linear complementarity problem is analyzed, where DðaÞ is composed of all feasible points with d-proximity to the central path less than or equal to a. The largest allowable value for a is 1.76. For a specific choice of a and a a lower bound of vn= ffiffiffi n p is obtained for the stepsize along the affine-scaling direction, where vn has an asymptotic value greater than 1.08. For nP 400 it is shown that vn > 1:05. The algorithm has Oð ffiffiffi n p LÞ-iteration complexity under general conditions and quadratic convergence under the strict complementarity assumption. 2002 Elsevier Science B.V. All rights reserved.