A full-Newton step feasible interior-point algorithm for monotone horizontal linear complementarity problems

In this paper, we present a full-Newton feasible step interior-point algorithm for solving monotone horizontal linear complementarity problems. In each iteration the algorithm performs only full-Newton step with the advantage that no line search is required. We prove under a new and appropriate strategy of the threshold that defines the size of the neighborhood of the central-path and of the update barrier parameter that the proposed algorithm is well-defined and the full-Newton step to the central-path is locally quadratically convergent. Moreover, we derive the complexity bound of the proposed algorithm with short-step method, namely, O(nlognϵ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {O}(\sqrt{n}\log \frac{n}{\epsilon })$$\end{document}. This bound is the currently best known iteration bound for monotone HLCP. Some numerical results are provided to show the efficiency of the proposed algorithm and to compare with an available method.