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.
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Acknowledgements
The research was partially supported Slovenian Research Agency with project grants N1-0071, J1-1693, J1-8132, J1-8130, J5-2552, J5-2512, P2-0162 and P2-0248, while the work of the Hungarian researchers who contributed instances and many useful ideas was partially supported by the Hungarian Research Fund, OTKA (grant no. NKFIH 125700).
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Povh, J., Žerovnik, J. On sufficient properties of sufficient matrices. Cent Eur J Oper Res 29, 809–822 (2021). https://doi.org/10.1007/s10100-021-00747-4
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DOI: https://doi.org/10.1007/s10100-021-00747-4