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.
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Acknowledgements
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, Innovación y Universidades (MCIU), the Agencia Estatal de Investigación (AEI), and the European Regional Development Fund (ERDF), and by the Australian Research Council, Project DP180100602.
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Dinh, N., Goberna, M.A., López, M.A., Volle, M. (2020). Characterizations of Robust and Stable Duality for Linearly Perturbed Uncertain Optimization Problems. In: Bailey, D., et al. From Analysis to Visualization. JBCC 2017. Springer Proceedings in Mathematics & Statistics, vol 313. Springer, Cham. https://doi.org/10.1007/978-3-030-36568-4_4
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