Abstract
In this note, we consider the linear complementarity problemw = Mz + q, w ≥ 0, z ≥ 0, w T z = 0, when all principal minors ofM are negative. We show that for such a problem for anyq, there are either 0, 1, 2, or 3 solutions. Also, a set of sufficiency conditions for uniqueness is stated.
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The work of both authors is partially supported by a grant from the National Science Foundation, MCS 77-03472.
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Kojima, M., Saigal, R. On the number of solutions to a class of linear complementarity problems. Mathematical Programming 17, 136–139 (1979). https://doi.org/10.1007/BF01588239
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DOI: https://doi.org/10.1007/BF01588239