Path-following interior point algorithms for the Cartesian P*(κ)-LCP over symmetric cones

In this paper, we establish a theoretical framework of path-following interior point algorithms for the linear complementarity problems over symmetric cones (SCLCP) with the Cartesian P _*(κ)-property, a weaker condition than the monotonicity. Based on the Nesterov-Todd, xy and yx directions employed as commutative search directions for semidefinite programming, we extend the variants of the short-, semilong-, and long-step path-following algorithms for symmetric conic linear programming proposed by Schmieta and Alizadeh to the Cartesian P _*(κ)-SCLCP, and particularly show the global convergence and the iteration complexities of the proposed algorithms. This work was supported by National Natural Science Foundation of China (Grant Nos. 10671010, 70841008)