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Large-Neighborhood Infeasible Predictor–Corrector Algorithm for Horizontal Linear Complementarity Problems over Cartesian Product of Symmetric Cones

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Abstract

We present an infeasible interior-point predictor–corrector algorithm, based on a large neighborhood of the central path, for horizontal linear complementarity problem over the Cartesian product of symmetric cones. Throughout the paper, we assume that a certain property holds for the above-mentioned problem. This condition is equivalent to the property of sufficiency for the particular case of horizontal linear complementarity problem. The polynomial convergence is shown for the commutative class of search directions. We specialize our algorithm further by prescribing some scaling elements and also consider the case of feasible starting points. We believe this to be the first interior-point method based on large neighborhoods for the problem in consideration.

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Acknowledgements

The authors are grateful to the referees and the editor for helpful comments to improve the presentation of the paper. The third author was supported by a Grant of the Romanian Ministry of Research and Innovation, CNCS - UEFISCDI, Project number PN-III-P4-ID-PCE-2016-0190, within PNCDI III. The second and fourth authors thank Shahrekord University and the fifth author thanks Research Council of Sharif University of Technology for financial support. The second and fourth authors were also partially supported by the Center of Excellence for Mathematics, University of Shahrekord, Shahrekord, Iran.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, Shahrekord, Iran

    Soodabeh Asadi, Hossein Mansouri & Maryam Zangiabadi

  2. Faculty of Mathematics and Computer Science, Babes-Bolyai University, No. 1 Mihail Kogalniceanu Street, 400084, Cluj-Napoca, Romania

    Zsolt Darvay

  3. Faculty of Mathematical Sciences, Sharif University of Technology, Tehran, Iran

    Nezam Mahdavi-Amiri

Authors
  1. Soodabeh Asadi
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  2. Hossein Mansouri
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  3. Zsolt Darvay
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  4. Maryam Zangiabadi
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  5. Nezam Mahdavi-Amiri
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Correspondence to Hossein Mansouri.

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Communicated by Alexey F. Izmailov.

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Asadi, S., Mansouri, H., Darvay, Z. et al. Large-Neighborhood Infeasible Predictor–Corrector Algorithm for Horizontal Linear Complementarity Problems over Cartesian Product of Symmetric Cones. J Optim Theory Appl 180, 811–829 (2019). https://doi.org/10.1007/s10957-018-1402-6

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  • DOI: https://doi.org/10.1007/s10957-018-1402-6

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