Complexity of a predictor-corrector interior-point method using special kernel function for sufficient WLCPs

A predictor-corrector interior-point method (PC IPM) is developed in this paper to address sufficient weighted linear complementarity problems (WLCPs). Specifically, the analysis is conducted by choosing the parameters of the kernel function $\phi \left(t\right)=\frac{t^{\mathfrak{p}+1}-1}{\mathfrak{p}+1}+\frac{t^{1-\mathfrak{q}}-1}{\mathfrak{q}-1}$ to $\mathfrak{p}=1$ and $\mathfrak{q}=3$. Each iteration of the algorithm performs two steps: a predictor step followed by a corrector step. Furthermore, with appropriate parameter selections, we prove that the proposed method remains strictly feasible and converges. A polynomial complexity bound is derived, which is comparable to the best-known iteration bound reported in the literature on PC IPMs for solving sufficient WLCPs. Additionally, preliminary numerical experiments indicate that the proposed algorithm performs effectively.