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A Polynomial Interior-Point Algorithm for Monotone Linear Complementarity Problems

Author

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  • H. Mansouri

    (Shahrekord University)

  • M. Pirhaji

    (Shahrekord University)

Abstract

In this paper, we propose an interior-point algorithm for monotone linear complementarity problems. The algorithm is based on a new technique for finding the search direction and the strategy of the central path. At each iteration, we use only full-Newton steps. Moreover, it is proven that the number of iterations of the algorithm coincides with the well-known best iteration bound for monotone linear complementarity problems.

Suggested Citation

  • H. Mansouri & M. Pirhaji, 2013. "A Polynomial Interior-Point Algorithm for Monotone Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 157(2), pages 451-461, May.
    • Handle: RePEc:spr:joptap:v:157:y:2013:i:2:d:10.1007_s10957-012-0195-2
    DOI: 10.1007/s10957-012-0195-2
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    References listed on IDEAS

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    1. Filiz Gurtuna & Cosmin Petra & Florian Potra & Olena Shevchenko & Adrian Vancea, 2011. "Corrector-predictor methods for sufficient linear complementarity problems," Computational Optimization and Applications, Springer, vol. 48(3), pages 453-485, April.
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    Cited by:

    1. Tibor Illés & Petra Renáta Rigó & Roland Török, 2024. "Unified Approach of Interior-Point Algorithms for $$P_*(\kappa )$$ P ∗ ( κ ) -LCPs Using a New Class of Algebraically Equivalent Transformations," Journal of Optimization Theory and Applications, Springer, vol. 202(1), pages 27-49, July.
    2. Behrouz Kheirfam, 2024. "Complexity Analysis of a Full-Newton Step Interior-Point Method for Monotone Weighted Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 202(1), pages 133-145, July.
    3. Darvay, Zsolt & Illés, Tibor & Rigó, Petra Renáta, 2022. "Predictor-corrector interior-point algorithm for P*(κ)-linear complementarity problems based on a new type of algebraic equivalent transformation technique," European Journal of Operational Research, Elsevier, vol. 298(1), pages 25-35.
    4. Behrouz Kheirfam, 2014. "A New Complexity Analysis for Full-Newton Step Infeasible Interior-Point Algorithm for Horizontal Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 853-869, June.

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