A full-modified-Newton step \begin{document}$ O(n) $\end{document} infeasible interior-point method for the special weighted linear complementarity problem

The weighted complementarity problem (wCP) can be applied to a large variety of equilibrium problems in science, economics and engineering. Since formulating an equilibrium problem as a wCP may lead to highly efficient algorithms for its numerical solution, wCP is a nontrivial generalization of the complementarity problem. In this paper we consider a special weighted linear complementarity problem (wLCP), which is the more general optimization of the Fisher market equilibrium problem. A full-modified-Newton infeasible interior-point method (IIPM) for the special wLCP is proposed. The algorithm reformulates the central path of the perturbed problem as an equivalent system of equations, and uses only full-Newton steps at each iteration, so-called a feasibility step (i.e., a full-modified-Newton step) and several usual centering steps. The polynomial complexity of the algorithm is as good as the best known iteration bound for these types of IIPMs in linear optimization.