In this paper we generalize large-update primal-dual interior point methods for linear optimization problems in [2] to the $P_*(kappa)$ linear complementarity problems based on a new kernel function which includes the kernel function in [2] as a special case. The kernel function is neither self-regular nor eligible. Furthermore, we improve the complexity result in [2] from $O(sqrt[]{n}(log;n)^2;log;frac{n{mu}o}{epsilon})$ to $Osqrt[]{n}(log;n)log(log;n)log;frac{m{mu}o}{epsilon}$.