Corrector-predictor arc-search interior-point algorithm for $P_*(kappa)$-LCP acting in a wide neighborhood of the central path

In this paper, we propose an arc-search corrector-predictor interior-point method for solving $P_*(kappa)$-linear complementarity problems. The proposed algorithm searches the optimizers along an ellipse that is an approximation of the central path. The algorithm generates a sequence of iterates in the wide neighborhood of central path introduced by Ai and Zhang. The algorithm does not depend on the handicap $kappa$ of the problem, so that it can be used for any $P_*(kappa)$-linear complementarity problem. Based on the ellipse approximation of the central path and the wide neighborhood, we show that the proposed algorithm has $O((1+kappa)sqrt{n}L)$ iteration complexity, the best-known iteration complexity obtained so far by any interior-point method for solving $P_*(kappa)$-linear complementarity problems.