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The Generalized Linear Complementarity Problem: Least Element Theory and Z-Matrices

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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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Authors and Affiliations

  1. Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN, 37403, U.S.A

    Aniekan A. Ebiefung

  2. Department of Mathematical Sciences, Clemson University, Clemson, SC, 29631, U.S.A

    Michael M. Kostreva

Authors
  1. Aniekan A. Ebiefung
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  2. Michael M. Kostreva
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Ebiefung, A.A., Kostreva, M.M. The Generalized Linear Complementarity Problem: Least Element Theory and Z-Matrices. Journal of Global Optimization 11, 151–161 (1997). https://doi.org/10.1023/A:1008224418676

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  • DOI: https://doi.org/10.1023/A:1008224418676

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