In this paper, a primal-dual interior-point method equipped with various selections of the displacement step are derived for solving second-order cone programming problems. We first establish the existence and uniqueness of the optimal solution of the corresponding perturbed problem and then demonstrate its convergence to the optimal solution of the original problem. Next, we present four different selections to calculate the displacement step. We also establish the convergence of the proposed algorithm and present its complexity result. Finally, the four selections of calculating the displacement step are compared in numerical examples to show the efficiency of the proposed algorithm.
The University of Jordan. June 1, 2017