Predictor-corrector method for nonlinear complementarity problem

Abstract

Recently, Ye et al. proved that the predictor-corrector method proposed by Mizuno et al. maintains\(O\left( {\sqrt n L} \right)\)-iteration complexity while exhibiting the quadratic convergence of the dual gap to zero under very mild conditions. This impressive result becomes the best-known in the interior point methods. In this paper, we modify the predictor-corrector method and then extend it to solving the nonlinear complementarity problem. We prove that the new method has a\((\sqrt n \log ({1 \mathord{\left/ {\vphantom {1 \varepsilon }} \right. \kern-\nulldelimiterspace} \varepsilon }))\)-iteration complexity while maintaining the quadratic asymptotic convergence.