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On Semimonotone Matrices, $$R_0$$ R 0 -Matrices and Q-Matrices

Author

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  • Thiruvankatachari Parthasarathy

    (Chennai Mathematical Institute)

  • Gomatam Ravindran

    (Indian Statistical Institute)

  • Sunil Kumar

    (Indian Statistical Institute)

Abstract

In 1979, Pang proved that within the class of semimonotone matrices, $$R_0$$ R 0 -matrices are Q-matrices and conjectured that the converse is also true. Jeter and Pye gave a counterexample when $$n=5$$ n = 5 for the converse; namely, they gave a semimonotone matrix that is in Q but not in $$R_0$$ R 0 . In this paper, we prove this conjecture for semimonotone matrices of order $$n \le 3$$ n ≤ 3 and provide a counterexample when $$ n> 3$$ n > 3 , showing the sharpness of the result. We also provide an application of this result.

Suggested Citation

  • Thiruvankatachari Parthasarathy & Gomatam Ravindran & Sunil Kumar, 2022. "On Semimonotone Matrices, $$R_0$$ R 0 -Matrices and Q-Matrices," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 131-147, October.
    • Handle: RePEc:spr:joptap:v:195:y:2022:i:1:d:10.1007_s10957-022-02066-3
    DOI: 10.1007/s10957-022-02066-3
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