Infeasible Mehrotra-Type Predictor-Corrector Interior-Point Algorithm for the Cartesian P *(κ)-LCP Over Symmetric Cones

We propose an infeasible Mehrotra-type predictor-corrector algorithm with a new center parameter updating scheme for Cartesian P *(κ)-linear complementarity problem over symmetric cones. Based on the Nesterov-Todd direction, we show that the iteration-complexity bound of the proposed algorithm is 𝒪((1 + κ)3 r 2log e−1), where r is the rank of the associated Euclidean Jordan algebras and κ is the handicap of the problem and e > 0 is the required precision. Some numerical results are reported as well.