The Generalized Linear Complementarity Problem: Least Element Theory and Z-Matrices |
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| Authors: | Aniekan A. Ebiefung Michael M. Kostreva |
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| Affiliation: | (1) Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN, 37403, U.S.A;(2) Department of Mathematical Sciences, Clemson University, Clemson, SC, 29631, U.S.A |
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| Abstract: | Existence of solutions to the Generalized Linear Complementarity Problem (GLCP) is characterized when the associated matrix is a vertical blockZ-matrix. It is shown that if solutions exist, then one must be the leastelement of the feasible region. Moreover, the vertical block Z-matrixbelongs to the class of matrices where feasibility implies existence of asolution to the GLCP. The concept of sufficient matrices of class Z isinvestigated to obtain additional properties of the solution set. |
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| Keywords: | Complementarity problems Z-matrices least element theory |
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