Abstract
ABSTRACTIn 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.
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