Ye et al. proved that the predictor–corrector method proposed by Mizuno et al. maintains O(√nL)-iteration complexity while exhibiting the quadratic convergence of the dual gap to zero under very mild conditions. This impressive result becomes the best-known of the interior point methods. In this paper, they modify the predictor–corrector method and then extend it to solving the nonlinear complementarity problem. They prove that the new method has a (√nlog(1/ε))-iteration complexity while maintaining the quadratic asymptotic convergence.
