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On the continuity of the solution map in linear complementarity problems. (English) Zbl 0779.90074
Author’s abstract: The continuity properties of the solution map ${\cal S}:(M,q)\mapsto{\cal S}(M,q)$ are investigated, where ${\cal S}(M,q)$ denotes the solution set corresponding to the linear complementarity problem $\text{LCP}(M,q)$. A Robinson-type upper semicontinuity result is established for ${\cal S}$, and a generalization of the Mangasarian-Shiau result concerning the Lipschitzian property of ${\cal S}$ in the $q$- variable is proved. It is also shown that when the matrix is positive semidefinite (or more generally a $G$-matrix), the solution map is Lipschitz continuous with respect to the $q$-vector if and only if the matrix is a $P$-matrix.

90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)
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