Existence and uniqueness of solutions for the generalized linear complementarity problem |
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Authors: | G. J. Habetler B. P. Szanc |
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Affiliation: | (1) Mathematical Sciences Department, Rensselaer Polytechnic Institute, Troy, New York;(2) Department of Mathematics, Maryville University, St. Louis, Missouri |
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Abstract: | Cottle and Dantzig (Ref. 1) showed that the generalized linear complementarity problem has a solution for anyqRm ifM is a vertical blockP-matrix of type (m1,...,mn). They also extended known characterizations of squareP-matrices to vertical blockP-matrices.Here we show, using a technique similar to Murty's (Ref. 2), that there exists a unique solution for anyqRm if and only ifM is a vertical blockP-matrix of type (m1,...,mn). To obtain this characterization, we employ a generalization of Tucker's theorem (Ref. 3) and a generalization of a theorem initially introduced by Gale and Nikaido (Ref. 4). |
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Keywords: | Linear complementarity problems generalized linear complementarity P-matrices Tucker's theorem |
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