A Corrector-Predictor Interior-Point Algorithm for P∗(κ)-HLCPs Over Cartesian Product of Symmetric Cones. (2nd January 2017)

• Record Type: Journal Article
• Authors: Asadi, S.; Zangiabadi, M.; Mansouri, H.
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 1(2017)
• Page Start: 20
• Page End: 38
• Publication Date: 2017-01-02
• Subjects: Cartesian product of symmetric cones; complexity bound; Corrector-predictor method; Euclidean Jordan algebra; P∗(κ)-horizontal linear complementarity problem; 90C33 -- 90C51; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1232731
• Languages: English
• ISSNs: 0163-0563

Abstract

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.