A Full Nesterov-todd Step Infeasible Interior-point Algorithm for Symmetric Cone Linear Complementarity Problem

A full Nesterov-Todd (NT) step infeasible interior-point algorithm is proposed for solving monotone linear complementarity problems over symmetric cones by using Euclidean Jordan algebra. Two types of full NT-steps are used, feasibility steps and centering steps. The algorithm starts from strictly feasible iterates of a perturbed problem, and, using the central path and feasibility steps, finds strictly feasible iterates for the next perturbed problem. By using centering steps for the new perturbed problem, strictly feasible iterates are obtained to be close enough to the central path of the new perturbed problem. The starting point depends on two positive numbers ρp and ρd. The algorithm terminates either by finding an ε-solution or detecting that the symmetric cone linear complementarity problem has no optimal solution with vanishing duality gap satisfying a condition in terms of ρp and ρd. The iteration bound coincides with the best known bound for infeasible interior-point methods.