A Corrector-Predictor Interior-Point Algorithm for P∗(κ)-HLCPs Over Cartesian Product of Symmetric Cones. (2nd January 2017) - Asadi, S.; Zangiabadi, M.; Mansouri, H.
ABSTRACT: In this article, we present a corrector-predictor path-following interior-point algorithm for P ∗ ( 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, , where r is the rank of the associated Euclidean Jordan algebra and 𝜀 is a prescribed tolerance.