- Title
- Characterizations of robust and stable duality for linearly perturbed uncertain optimization problems
- Creator
- Dinh, Nguyen; Goberna, Miguel; López, Marco; Volle, Michel
- Date
- 2020
- Type
- Text; Conference paper
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/179024
- Identifier
- vital:15498
- Identifier
-
https://doi.org/10.1007/978-3-030-36568-4_4
- Identifier
- ISBN:2194-1009 (ISSN); 9783030365677 (ISBN)
- Abstract
- We introduce a robust optimization model consisting in a family of perturbation functions giving rise to certain pairs of dual optimization problems in which the dual variable depends on the uncertainty parameter. The interest of our approach is illustrated by some examples, including uncertain conic optimization and infinite optimization via discretization. The main results characterize desirable robust duality relations (as robust zero-duality gap) by formulas involving the epsilon-minima or the epsilon-subdifferentials of the objective function. The two extreme cases, namely, the usual perturbational duality (without uncertainty), and the duality for the supremum of functions (duality parameter vanishing) are analyzed in detail. © Springer Nature Switzerland AG 2020.
- Publisher
- Springer
- Relation
- Jonathan Borwein Commemorative Conference, JBCC 2017 Vol. 313, p. 43-74; 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 © Springer Nature Switzerland AG 2020
- Rights
- Open Access
- Subject
- Robust duality; Strong robust duality; Reverse strong robust duality; Min-max robust duality
- Full Text
- Reviewed
- Funder
- This research was supported by the Vietnam National University-HCM city, Vietnam, project B2019-28-02, by PGC2018-097960-B-C22 of the Ministerio de Ciencia, Innovaci?n y Universidades (MCIU), the Agencia Estatal de Investigaci?n (AEI), and the European Regional Development Fund (ERDF), and by the Australian Research Council, Project DP180100602.
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