An interior-point method for the Cartesian P*(k)-linear complementarity problem over symmetric cones

A novel primal-dual path-following interior-point algorithm for the Cartesian P*(k)-linear complementarity problem over symmetric cones is presented. The algorithm is based on a reformulation of the central path for finding the search directions. For a full Nesterov-Todd step feasible interior-point algorithm based on the new search directions, the complexity bound of the algorithm with small-update approach is the best-available bound.