Kernel-Based Full-Newton Step Feasible Interior-Point Algorithm for $$P_{*}(\kappa )$$ P ∗ ( κ ) -Weighted Linear Complementarity Problem

In this paper, we consider a kernel-based full-Newton step feasible interior-point method (IPM) for $$P_{*}(\kappa )$$ P ∗ ( κ ) -Weighted Linear Complementarity Problem (WLCP). The specific eligible kernel function is used to define an equivalent form of the central path, the proximity measure, and to obtain search directions. Full-Newton steps are adopted to avoid the line search at each iteration. It is shown that with appropriate choices of the parameters, and a certain condition on the starting point, the iterations always lie in the defined neighborhood of the central path. Assuming strict feasibility of $$P_{*}(\kappa )$$ P ∗ ( κ ) -WLCP, it is shown that the IPM converges to the $$\varepsilon $$ ε -approximate solution of $$P_{*}(\kappa )$$ P ∗ ( κ ) -WLCP in a polynomial number of iterations. Few numerical results are provided to indicate the computational performance of the algorithm.