- Title
- Lipschitz modulus of linear and convex inequality systems with the Hausdorff metric
- Creator
- Beer, Gerald; Cánovas, M. J.; López, Marco; Parra, Juan
- Date
- 2021
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/178581
- Identifier
- vital:15419
- Identifier
-
https://doi.org/10.1007/s10107-020-01543-9
- Identifier
- ISBN:0025-5610 (ISSN)
- Abstract
- This paper analyzes the Lipschitz behavior of the feasible set mapping associated with linear and convex inequality systems in Rn. To start with, we deal with the parameter space of linear (finite/semi-infinite) systems identified with the corresponding sets of coefficient vectors, which are assumed to be closed subsets of Rn+1. In this framework the size of perturbations is measured by means of the (extended) Hausdorff distance. A direct antecedent, extensively studied in the literature, comes from considering the parameter space of all linear systems with a fixed index set, T, where the Chebyshev (extended) distance is used to measure perturbations. In the present work we propose an appropriate indexation strategy which allows us to establish the equality of the Lipschitz moduli of the feasible set mappings in both parametric contexts, as well as to benefit from existing results in the Chebyshev setting for transferring them to the Hausdorff one. In a second stage, the possibility of perturbing directly the set of coefficient vectors of a linear system leads to new contributions on the Lipschitz behavior of convex systems via linearization techniques. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society. Correction: The article “Lipschitz modulus of linear and convex inequality systems with the Hausdorff metric”, written by Beer,G., Cánovas, M.J., López, M.A., Parra, J.was originally published Online First without Open Access. After publication in volume 189, issue 1–2, page 75–98 the author decided to opt for Open Choice and to make the article an Open Access publication. Therefore, the copyright of the article has been changed to © The Author(s) 2020 and the article is forthwith distributed under the terms of the Creative Commons Attribution 4.0 International License. https://doi.org/10.1007/s10107-021-01751-x
- Publisher
- Springer Science and Business Media Deutschland GmbH
- Relation
- Mathematical Programming Vol. 189, no. 1-2 (2021), p. 75-98. https://purl.org/au-research/grants/arc/DP180100602; http://purl.org/au-research/grants/arc/DP180100602
- Rights
- All metadata describing materials held in, or linked to, the repository is freely available under a CC0 licence
- Rights
- Copyright © 2021, The Author(s).
- Rights
- Open Access
- Subject
- 0102 Applied Mathematics; 0103 Numerical and Computational Mathematics; 0802 Computation Theory and Mathematics; Convex inequalities; Feasible set mapping; Hausdorff metric; Indexation; Lipschitz modulus
- Full Text
- Reviewed
- Funder
- This research has been partially supported by Grants MTM2014-59179-C2-(1-2)-P and PGC2018-097960-B-C2(1-2) from MINECO/MICINN, Spain, and ERDF, “A way to make Europe”, European Union. The third author was partially supported by the Australian Research Council, Project DP180100602.
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