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.

In this paper, we present a predictor-corrector interior-point algorithm for $P_{\ast }(\kappa )$-weighted linear complementarity problems. Based on the kernel function $\phi (t)=\sqrt{t}$, the search direction of the algorithm is obtained. By choosing appropriate parameters, we prove that the algorithm is feasible and convergent. It is shown that the proposed algorithm has polynomial iteration complexity. Numerical results illustrate the effectiveness of the algorithm.