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

Author

Listed:
  • Soodabeh Asadi

    (Shahrekord University)

  • Hossein Mansouri

    (Shahrekord University)

  • Zsolt Darvay

    (Babes-Bolyai University)

  • Maryam Zangiabadi

    (Shahrekord University)

  • Nezam Mahdavi-Amiri

    (Sharif University of Technology)

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.

Suggested Citation

  • Soodabeh Asadi & Hossein Mansouri & Zsolt Darvay & Maryam Zangiabadi & Nezam Mahdavi-Amiri, 2019. "Large-Neighborhood Infeasible Predictor–Corrector Algorithm for Horizontal Linear Complementarity Problems over Cartesian Product of Symmetric Cones," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 811-829, March.
    • Handle: RePEc:spr:joptap:v:180:y:2019:i:3:d:10.1007_s10957-018-1402-6
    DOI: 10.1007/s10957-018-1402-6
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    References listed on IDEAS

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    1. Shinji Mizuno & Michael J. Todd & Yinyu Ye, 1993. "On Adaptive-Step Primal-Dual Interior-Point Algorithms for Linear Programming," Mathematics of Operations Research, INFORMS, vol. 18(4), pages 964-981, November.
    2. Yu. E. Nesterov & M. J. Todd, 1997. "Self-Scaled Barriers and Interior-Point Methods for Convex Programming," Mathematics of Operations Research, INFORMS, vol. 22(1), pages 1-42, February.
    3. Gu, G. & Zangiabadi, M. & Roos, C., 2011. "Full Nesterov-Todd step infeasible interior-point method for symmetric optimization," European Journal of Operational Research, Elsevier, vol. 214(3), pages 473-484, November.
    4. Hongwei Liu & Ximei Yang & Changhe Liu, 2013. "A New Wide Neighborhood Primal–Dual Infeasible-Interior-Point Method for Symmetric Cone Programming," Journal of Optimization Theory and Applications, Springer, vol. 158(3), pages 796-815, September.
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    Cited by:

    1. Marianna E.-Nagy & Anita Varga, 2024. "A New Ai–Zhang Type Interior Point Algorithm for Sufficient Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 202(1), pages 76-107, July.

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