A new interior-point algorithm for P∗(k)-NCP based on a class of parametric kernel functions

In this paper, we propose a long step interior point algorithm for solving the P∗(k)-nonlinear complementarity problem (NCP) based on a new class of parametric kernel functions. A simple analysis shows that if a strictly feasible starting point is available and the problem satisfies certain conditions, then the proposed algorithm has O((1+2k)nlognlog(nμ0/ε)) iteration complexity. This result coincides with the current best-known iteration bounds for such methods.