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On sufficient properties of sufficient matrices

Author

Listed:
  • Janez Povh

    (University of Ljubljana)

  • Janez Žerovnik

    (University of Ljubljana)

Abstract

In this paper we study sufficient matrices, which play an important role in theoretical analysis of interior-point methods for linear complementarity problems. We present new characterisations of these matrices which imply new necessary and sufficient conditions for sufficiency. We use these results to develop an algorithm with exponential iteration complexity which in each iteration solves a simple instance of linear programming problem and is capable to reveal whether given symmetric matrix is sufficient or not. This algorithm demonstrates 100 % accuracy on all tested instances of matrices.

Suggested Citation

  • Janez Povh & Janez Žerovnik, 2021. "On sufficient properties of sufficient matrices," 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. 29(3), pages 809-822, September.
    • Handle: RePEc:spr:cejnor:v:29:y:2021:i:3:d:10.1007_s10100-021-00747-4
    DOI: 10.1007/s10100-021-00747-4
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    References listed on IDEAS

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    1. Carmo Brás & Gabriele Eichfelder & Joaquim Júdice, 2016. "Copositivity tests based on the linear complementarity problem," Computational Optimization and Applications, Springer, vol. 63(2), pages 461-493, March.
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    Cited by:

    1. Andrej Kastrin & Janez Povh & Lidija Zadnik Stirn & Janez Žerovnik, 2021. "Methodologies and applications for resilient global development from the aspect of SDI-SOR special issues of CJOR," 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. 29(3), pages 773-790, September.
    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. Milan Hladík, 2021. "Stability of the linear complementarity problem properties under interval uncertainty," 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. 29(3), pages 875-889, September.

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