Positive subdefinite matrices, generalized monotonicity, and linear complementarity problems (Q2706242)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Positive subdefinite matrices, generalized monotonicity, and linear complementarity problems |
scientific article |
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19 March 2001
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positive subdefiniteness
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copositivity
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copositivity star
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generalized monotonicity
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linear complementarity
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Positive subdefinite matrices, generalized monotonicity, and linear complementarity problems (English)
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Extending the notion introduced by \textit{B. Martos} [SIAM J. Appl. Math. 17, 1215-1223 (1969; Zbl 0186.34201)] for symmetric matrices, a (possibly nonsymmetric) \(n\times n\) real matrix \(M\) is called positive subdefinite (PSBD) if \(\langle z,Mz\rangle< 0\) implies either \(M^tz\leq 0\) or \(M^t z\geq 0\). The authors give some characterizations of PSBD matrices and use them to study generalized monotonicity properties of affine maps on the nonnegative orthant and to describe the solution sets to linear complementarity problems in some special cases.
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