- Title
- A note on primal-dual stability in infinite linear programming
- Creator
- Goberna, Miguel; López, Marco; Ridolfi, Andrea; Vera de Serio, Virginia
- Date
- 2020
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/174098
- Identifier
- vital:14766
- Identifier
-
https://doi.org/10.1007/s11590-020-01549-4
- Identifier
- ISBN:1862-4472 (ISSN)
- Abstract
- In this note we analyze the simultaneous preservation of the consistency (and of the inconsistency) of linear programming problems posed in infinite dimensional Banach spaces, and their corresponding dual problems, under sufficiently small perturbations of the data. We consider seven different scenarios associated with the different possibilities of perturbations of the data (the objective functional, the constraint functionals, and the right hand-side function), i.e., which of them are known, and remain fixed, and which ones can be perturbed because of their uncertainty. The obtained results allow us to give sufficient and necessary conditions for the coincidence of the optimal values of both problems and for the stability of the duality gap under the same type of perturbations. There appear substantial differences with the finite dimensional case due to the distinct topological properties of cones in finite and infinite dimensional Banach spaces. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature.; Funding details: Australian Research Council, ARC, DP180100602: http://purl.org/au-research/grants/arc/DP180100602
- Publisher
- Springer Science and Business Media Deutschland GmbH
- Relation
- Optimization Letters Vol. 14, no. 8 (2020), p. 2247-2263
- Rights
- Copyright © 2020 Springer Nature Switzerland AG
- Rights
- This metadata is freely available under a CCO license
- Subject
- 0102 Applied Mathematics; 0103 Numerical and Computational Mathematics; Consistency; Inconsistency; Infinite dimensions; Linear programming; Primal-dual stability
- Reviewed
- Funder
- Funding details: Australian Research Council, ARC, DP180100602: http://purl.org/au-research/grants/arc/DP180100602
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