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Ky Fan's N-matrices and linear complementarity problems

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Abstract

We consider the linear complementarity problem (LCP),w=Az + q, w⩾0,z⩾0,w T z=0, when all the off-diagonal entries ofA are nonpositive (the class of Z-matrices), all the proper principal minors ofA are positive and the determinant ofA is negative (the class of almost P-matrices). We shall call this the class of F-matrices. We show that ifA is a Z-matrix, thenA is an F-matrix if and only if LCP(q, A) has exactly two solutions for anyq⩾0,q≠0, and has at most two solutions for any otherq.

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Authors and Affiliations

  1. RUTCOR Rutgers Center for Operations Research, Rutgers University, P.O. Box 5062, 08903-5062, New Brunswick, NJ, USA

    Jianming Miao

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  1. Jianming Miao
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Research supported by AFOSR-89-0512.

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Miao, J. Ky Fan's N-matrices and linear complementarity problems. Mathematical Programming 61, 351–356 (1993). https://doi.org/10.1007/BF01582156

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  • DOI: https://doi.org/10.1007/BF01582156

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