On the Parametric Linear Complementarity Problem

R. A. Danao

Journal of Optimization Theory and Applications, 1997, vol. 95, issue 2, No 12, 445-454

Abstract: Abstract Consider the parametric linear complementarity problem w=Mz+q+λp, w≥0, z≥0, w T z=0, where p≠0, 0≠q≥0, and λ≥0. We show that a necessary condition for every complementary map z(λ) to be isotone for every nonzero q≥0 and every p is that M be either a P-matrix or a $$P_{{\text{ }}1}^* $$ -matrix. The Cottle necessary and sufficient conditions for strong and uniform isotonicity for P-matrices are restated, with slight modifications, for $$P_{{\text{ }}1}^* $$ -matrices.

Keywords: Parametric linear complementarity problem; isotone solutions; matrices; complementary cones (search for similar items in EconPapers)
Date: 1997
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DOI: 10.1023/A:1022699624785

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