A Second-order Corrector Infeasible Interior-point Method with One-norm wide Neighborhood for Symmetric Optimization

Abstract

In this article, we present a second-order corrector infeasible interior-point method based on one-norm large neighborhood for symmetric optimization. We consider the classical Newton direction as the sum of two other directions associated with the negative and positive parts of the right-hand side of the centrality equation. In addition to equipping them with different step lengths, we add a corrector step that is multiplied by the square of the step length in the expression of the new iterate. The convergence analysis of the algorithm is discussed and it is proved that the new algorithm has the same complexity as small neighborhood infeasible interiorpoint algorithms for the Nesterov-Todd (NT) direction, and the xs and sx directions.