Abstract
The present paper deals with uncertain linear inequality systems viewed as nonempty closed coefficient sets in the \(\left( n+1\right) \)-dimensional Euclidean space. The perturbation size of these uncertainty sets is measured by the (extended) Hausdorff distance. We focus on calmness constants—and their associated neighborhoods—for the feasible set mapping at a given point of its graph. To this aim, the paper introduces an appropriate indexation function which allows us to provide our aimed calmness constants through their counterparts in the setting of linear inequality systems with a fixed index set, where a wide background exists in the literature.
Dedicated to the memory of Pedro Gil
This research has been partially supported by Grant MTM2014-59179-C2-(1-2)-P from MINECO, Spain, and FEDER “Una manera de hacer Europa”, European Union, and by the Australian Research Council, Project DP160100854.
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Cánovas, M.J., Henrion, R., López, M.A., Parra, J. (2018). Indexation Strategies and Calmness Constants for Uncertain Linear Inequality Systems. In: Gil, E., Gil, E., Gil, J., Gil, M. (eds) The Mathematics of the Uncertain. Studies in Systems, Decision and Control, vol 142. Springer, Cham. https://doi.org/10.1007/978-3-319-73848-2_76
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DOI: https://doi.org/10.1007/978-3-319-73848-2_76
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