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On the Connectedness of Solution Sets of Parametrized Equations and of Solution Sets in Linear Complementarity Problems

  • M. Seetharama Gowda
  • G. S. R. Murthy
  • T. Parthasarathy
Part of the Applied Optimization book series (APOP, volume 50)

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 AP 0Q, C = 0, and D is connected. We also show that (a) any nonnegative P 0Q 0-matrix is connected and (b) any matrix M partitioned as above with C and D nonnegative, and AP 0Q is connected.

Keywords

Linear complementarity problem solution sets connectedness weak univalence 

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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • M. Seetharama Gowda
    • 1
  • G. S. R. Murthy
    • 2
  • T. Parthasarathy
    • 3
  1. 1.Department of Mathematics and StatisticsUniversity of MarylandBaltimore County, BaltimoreUSA
  2. 2.Indian Statistical InstituteHabsiguda, HyderabadIndia
  3. 3.Indian Statistical InstituteNew DelhiIndia

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