Infeasible path-following interior point algorithm for Cartesian P*() nonlinear complementarity problems over symmetric cones

In this paper, we establish a theoretical framework of infeasible path-following interior point algorithm for Cartesian inline-graphic> nonlinear complementarity problems over symmetric cones using a wide neighbourhood of the central path. In order to prove the convergence of the proposed algorithm, we propose a scaled Lipschitz condition which has scaling invariance. Under the condition, we estimate the iteration complexities of the proposed algorithm and provide some numerical results. The numerical results show that the algorithm is efficient and reliable.