Set-Valued and Variational Analysis

, Volume 22, Issue 2, pp 375–389 | Cite as

Calmness of the Feasible Set Mapping for Linear Inequality Systems

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

Abstract

In this paper we deal with parameterized linear inequality systems in the n-dimensional Euclidean space, whose coefficients depend continuosly on an index ranging in a compact Hausdorff space. The paper is developed in two different parametric settings: the one of only right-hand-side perturbations of the linear system, and that in which both sides of the system can be perturbed. Appealing to the backgrounds on the calmness property, and exploiting the specifics of the current linear structure, we derive different characterizations of the calmness of the feasible set mapping, and provide an operative expresion for the calmness modulus when confined to finite systems. In the paper, the role played by the Abadie constraint qualification in relation to calmness is clarified, and illustrated by different examples. We point out that this approach has the virtue of tackling the calmness property exclusively in terms of the system’s data.

Keywords

Calmness Local error bounds Variational analysis Semi-infinite programming Linear programming Feasible set mapping 

Mathematics Subject Classifications (2010)

90C34 90C31 49J53 90C05 

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • M. J. Cánovas
    • 1
  • M. A. López
    • 2
    • 3
  • J. Parra
    • 1
  • F. J. Toledo
    • 1
  1. 1.Center of Operations ResearchMiguel Hernández University of ElcheElcheSpain
  2. 2.Department of Statistics and Operations ResearchUniversity of AlicanteAlicanteSpain
  3. 3.Federation University of AustraliaBallaratAustralia

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