A strongly sub-feasible primal-dual quasi interior-point algorithm for nonlinear inequality constrained optimization

In this paper, a primal-dual quasi interior-point algorithm for inequality constrained optimization problems is presented. At each iteration, the algorithm solves only two or three reduced systems of linear equations with the same coefficient matrix. The algorithm starts from an arbitrarily initial point. Then after finite iterations, the iteration points enter into the interior of the feasible region and the objective function is monotonically decreasing. Furthermore, the proposed algorithm is proved to possess global and superlinear convergence under mild conditions including a weak assumption of positive definiteness. Finally, some encouraging preliminary computational results are reported.