An Arc Search Interior-Point Algorithm for Monotone Linear Complementarity Problems over Symmetric Cones

An arc search interior-point algorithm for monotone symmetric cone linear complementarity problem is presented. The algorithm estimates the central path by an ellipse and follows an ellipsoidal approximation of the central path to reach an epsilon-approximate solution of the problem in a wide neighborhood of the central path. The convergence analysis of the algorithm is derived. Furthermore, we prove that the algorithm has the complexity bound O(root rL) using Nesterov-Todd search direction and O(rL) by the xs and sx search directions. The obtained iteration complexities coincide with the best-known ones obtained by any proposed interior point algorithm for this class of mathematical problems.