- Title
- Calmness of the feasible set mapping for linear inequality systems
- Creator
- Cánovas, Maria; López, Marco; Parra, Juan; Toledo, Javier
- Date
- 2014
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/65678
- Identifier
- vital:5902
- Identifier
-
https://doi.org/10.1007/s11228-014-0272-9
- Identifier
- ISSN:0927-6947
- 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.
- Publisher
- Springer Science and Business Media Netherlands
- Relation
- Set-Valued and Variational Analysis Vol. 22, no. 2 (2014), p. 375-389; http://purl.org/au-research/grants/arc/DP110102011
- Rights
- © Springer Science+Business Media Dordrecht 2014
- Rights
- This metadata is freely available under a CCO license
- Subject
- 0101 Pure Mathematics; Calmness; Local error bounds; Variational analysis; Semi-infinite programming; Linear programming; Feasible set mapping
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