The weighted complementarity problem (WCP) aims at finding a pair of vectors belonging to the intersection of a manifold and a cone, such that the product of the vectors under a certain algebra equals a given weighted vector. As a nontrivial generalization of complementarity problems, WCP can be used to solve various equilibrium problems in science, economics and engineering, which in some cases may lead to highly efficient algorithms. Considering a weighted linear complementarity problem (WLCP) over the nonnegative orthant, an improved full-Newton step infeasible interior point algorithm is presented for its numerical solution. By extending a full-Newton infeasible interior-point algorithm for linear optimization, the perturbed problem of WLCP, its central path, and the induced Newton direction are introduced. The algorithm constructs strictly feasible iterates for a sequence of perturbed problems of WLCP. Each main iteration of the algorithm consists of one feasibility step and several central steps, which uses only full-Newton steps, and therefore it is not necessary to calculate the steplength; at each iteration, the algorithm reduces the feasibility residuals and the weight vector residuals at the same rate; based on the quadratic convergence result of the central step, a slightly wider neighborhood is provided for the feasibility step. The feasibility step, centering step and convergence are anaylzed. Then the algorithm is shown to possess global convergence and polynomial-time complexity. Finally, some numerical examples illustrate the efficiency of the proposed algorithm for solving WLCP.
