On the number of solutions to a class of linear complementarity problems
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In this note, we consider the linear complementarity problemw = Mz + q, w ≥ 0, z ≥ 0, wTz = 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.
[1] M. Shubik,et al. Convex structures and economic theory , 1968 .
[2] R. Saigal. On the Alass of Complementary Cones and Lemke’s Algorithm , 1972 .
[3] Katta G. Murty,et al. On the number of solutions to the complementarity problem and spanning properties of complementary cones , 1972 .
[4] M. Kojima,et al. A Study of ${\text{PC}}^1 $ Homeomorphisms on Subdivided Polyhedrons , 1979 .
[5] H. Samelson,et al. A partition theorem for Euclidean $n$-space , 1958 .