Stability of Linear Inequality Systems in a Parametric Setting

  • M. J. Cánovas
  • M. A. López
  • J. Parra
Article

DOI: 10.1007/s10957-004-1838-8

Cite this article as:
Cánovas, M.J., López, M.A. & Parra, J. J Optim Theory Appl (2005) 125: 275. doi:10.1007/s10957-004-1838-8

Abstract

In this paper, we propose a parametric approach to the stability theory for the solution set of a semi-infinite linear inequality system in the n-dimensional Euclidean space \({\mathbb R}^{n}\). The main feature of this approach is that the coefficient perturbations are modeled through the so-called mapping of parametrized systems, which assigns to each parameter, ranging in a metric space, a subset of \({\mathbb R}^{n+1}\). Each vector of this image set provides the coefficients of an inequality in \({\mathbb R}^{n}\) and the whole image set defines the inequality system associated with the parameter. Thus, systems associated with different parameters are not required to have the same number (cardinality) of inequalities. The paper is focused mainly on the structural stability of the feasible set mapping, providing a characterization of the Berge lower-semicontinuity property. The role played by the strong Slater qualification is analyzed in detail.

Keywords

Stability parametrized systems linear inequality systems feasible set mapping 

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • M. J. Cánovas
    • 1
  • M. A. López
    • 2
  • J. Parra
    • 1
  1. 1.Associate Professor, Operations Research CenterMiguel Hernández University of ElcheAlicanteSpain
  2. 2.Professor, Department of Statistics and Operations ResearchUniversity of AlicanteAlicanteSpain

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