On the convergence analysis of arc search interior point methods for LCPs

Following the central-path, as a guide line to optimal solution of mathematical problems, is one of the main difficulty of interior-point methods in practice. These iterative methods, follow the central path step by step to get close enough to the optimal solution of underlying problem. Based on estimating the central path by an ellipse, we propose an infeasible interior-point method for linear complementarity problem. In each iteration, the algorithm follows the ellipsoidal approximation of the central-path to find an ε -approximate solution of the problem. We prove that under certain conditions the proposed algorithm is well-defined and the generated points by the algorithm converge to an ε -approximate solution of the linear complementarity problem.