A feasible interior-point method with full-Newton step for P*(κ)-weighted linear complementarity problem via the algebraically equivalent transformation

This paper investigates feasible interior-point method (IPM) with full-Newton step for P*(κ)-weighted linear complementarity problem (WLCP). In particular, by applying the algebraically equivalent transformation (AET) for linear optimization, we obtain the new search directions by solving the perturbed Newton system. The AET of the Newton system is based on the kernel function φ(t)=t−t, which is used for solving WLCP for the first time. At each iteration, our algorithm takes only full-Newton steps. Therefore, no line-searches are needed to update the iterates. We show the strict feasibility of the full-Newton step and the polynomial iteration complexity of our algorithm under suitable assumptions. Some numerical experiments demonstrate the effectiveness of the proposed algorithm.