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- W182693257 abstract "In this article, we prove, under certain conditions, the connectedness of sets of the form {x: f(x, y) = 0, y ∈ E} where f is a function with x varying over an open set in R n and the parameter y varying over a topological space. Based on this, we show that the partitioned matrix $$M = left[ begin{gathered} A,,,,,,B hfill B,,,,,,D hfill end{gathered} right]$$ is (LCP) connected (i.e., for all q, the solution set of LCP(q, M) is connected) when A ∈ P 0 ∩ Q, C = 0, and D is connected. We also show that (a) any nonnegative P 0 ∩ Q 0-matrix is connected and (b) any matrix M partitioned as above with C and D nonnegative, and A ∈ P 0 ∩ Q is connected.KeywordsLinear complementarity problemsolution setsconnectednessweak univalence" @default.
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- W182693257 date "2001-01-01" @default.
- W182693257 modified "2023-09-27" @default.
- W182693257 title "On the Connectedness of Solution Sets of Parametrized Equations and of Solution Sets in Linear Complementarity Problems" @default.
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- W182693257 doi "https://doi.org/10.1007/978-1-4757-3279-5_8" @default.
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