An Adaptive Primal-Dual Full-Newton Step Infeasible Interior-Point Algorithm for Linear Optimization

Abstract

Abstract. In this paper, we improve the full-Newton step infeasible interior-point algorithm proposed by Mansouri et al. [6]. The algorithm takes only one full-Newton step in a major iteration. To perform this step, the algorithm adopts the largest logical value for the barrier update parameter θ. This value is adapted with the value of proximity function δ related to (x, y, s) in current iteration of the algorithm. We derive a suitable interval to change the parameter θ from iteration to iteration. This leads to more flexibilities in the algorithm, compared to the situation that θ takes a default fixed value.