New path-following interior-point algorithms for P∗(κ)P∗(κ)-nonlinear complementarity problems

In this paper, we propose new large-update path-following interior-point algorithms for P∗(κ)P∗(κ)-nonlinear complementarity problems (NCPs). We define new classes of parametric kernel functions and based on these functions new search directions and proximity measures are defined. We show that if a strictly feasible starting point is available and the undertaken problem satisfies certain conditions, then new large-update path-following interior-point algorithms for P∗(κ)P∗(κ)-NCPs have O((1+2κ)nlognlognμ0ε) iteration complexity which is currently the best known result for such methods.