Search

In this article, we present a corrector-predictor path-following interior-point algorithm forP∗(κ)-horizontal linear complementarity problem over Cartesian product of symmetric cones, using Euclidean Jordan algebras. This comprehensive problem is a newly introduced problem in the context of interior-point methods. The algorithm takes damped Nesterov-Todd steps in the predictor (affine-scaling) stage while maintaining a certain neighborhood of the central path. Moreover, at each corrector stage, we use only full-Nesterov-Todd steps. Furthermore, we derive the currently best known iteration bound for the algorithm with small updates, namely,, whereris the rank of the associated Euclidean Jordan algebra and𝜀is a prescribed tolerance. [ABSTRACT FROM AUTHOR]

In this article, we present a new predictor-corrector interior-point method, based on a wide neighborhood of the central path, for linear programming problems. In the corrector step ofthe proposed method, we derive the step size and corrector directions that guarantee that each iteration lies in a wide neighborhood of the central path. We also prove that the algorithm hasiteration complexity, which coincides with the best bound derived for linear programming problems. [ABSTRACT FROM PUBLISHER]