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EP Theorem for Dual Linear Complementarity Problems

Author

Listed:
  • T. Illés

    (Strathclyde University)

  • M. Nagy

    (Eötvös Lorànd University of Science)

  • T. Terlaky

    (School of Computational Engineering and Science, McMaster University)

Abstract

The linear complementarity problem (LCP) belongs to the class of $\mathbb{NP}$ -hard problems. Therefore, we cannot expect a polynomial time solution method for LCPs without requiring some special property of the matrix of the problem. We show that the dual LCP can be solved in polynomial time if the matrix is row sufficient; moreover, in this case, all feasible solutions are complementary. Furthermore, we present an existentially polytime (EP) theorem for the dual LCP with arbitrary matrix.

Suggested Citation

  • T. Illés & M. Nagy & T. Terlaky, 2009. "EP Theorem for Dual Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 140(2), pages 233-238, February.
    • Handle: RePEc:spr:joptap:v:140:y:2009:i:2:d:10.1007_s10957-008-9440-0
    DOI: 10.1007/s10957-008-9440-0
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    Citations

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    Cited by:

    1. 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.
    2. Marianna E.-Nagy & Tibor Illés & Janez Povh & Anita Varga & Janez Žerovnik, 2024. "Sufficient Matrices: Properties, Generating and Testing," Journal of Optimization Theory and Applications, Springer, vol. 202(1), pages 204-236, July.
    3. Zsolt Darvay & Petra Renáta Takács, 2018. "Large-step interior-point algorithm for linear optimization based on a new wide neighbourhood," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(3), pages 551-563, September.
    4. Petra Renáta Rigó & Zsolt Darvay, 2018. "Infeasible interior-point method for symmetric optimization using a positive-asymptotic barrier," Computational Optimization and Applications, Springer, vol. 71(2), pages 483-508, November.

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