Abstract
We give a short proof of the finiteness of Murty's principal pivoting algorithm for solving the linear complementarity problemy = Mz + q, y T z = 0,y ≥ 0,z ≥ 0 withP-matrixM.
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References
M. Fiedler and V. Pták, “On matrices with non-positive off-diagonal elements and positive principal minors,”Czechoslovak Mathematical Journal 12 (1962) 382–400.
K.G. Murty, “Note on a Bard-type scheme for solving the complementarity problem,”Opsearch 11 (1974) 123–130.
K.G. Murty, “Computational complexity of complementary pivot methods,”Mathematical Programming Study 7 (1978) 61–73.
A.W. Tucker, “Principal pivotal transforms of square matrices,”SIAM Review 5 (1963) 305.
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Rohn, J. A short proof of finiteness of Murty's principal pivoting algorithm. Mathematical Programming 46, 255–256 (1990). https://doi.org/10.1007/BF01585743
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DOI: https://doi.org/10.1007/BF01585743