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

Thiruvankatachari Parthasarathy (), Gomatam Ravindran () and Sunil Kumar ()
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Thiruvankatachari Parthasarathy: Chennai Mathematical Institute
Gomatam Ravindran: Indian Statistical Institute
Sunil Kumar: Indian Statistical Institute

Journal of Optimization Theory and Applications, 2022, vol. 195, issue 1, No 5, 147 pages

Abstract: 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.

Keywords: Q matrices; $$R_0$$ R 0 matrices; Semimonotone matrices; Copositive matrices; Principal pivot transform; Completely mixed games; 90C33; 91A05 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-022-02066-3

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