Abstract
This paper considers an uncertain convex optimization problem, posed in a locally convex decision space with an arbitrary number of uncertain constraints. To this problem, where the uncertainty only affects the constraints, we associate a robust (pessimistic) counterpart and several dual problems. The paper provides corresponding dual variational principles for the robust counterpart in terms of the closed convexity of different associated cones.
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Acknowledgements
The authors are grateful to the referees for their constructive comments and helpful suggestions which have contributed to the final preparation of the paper. This research was supported by the National Foundation for Science and Technology Development (NAFOSTED) of Vietnam, Project 101.01-2015.27, Generalizations of Farkas lemma with applications to optimization, by the Ministry of Economy and Competitiveness of Spain and the European Regional Development Fund (ERDF) of the European Commission, ProjectMTM2014-59179-C2-1-P, and by the Australian Research Council, Project DP160100854. Parts of the work of the first author were developed during his visit to the Department of Mathematics, University of Alicante, in July 2016, for which he would like to express his sincere thanks to the support and the hospitality he received.
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Communicated by Radu Ioan Bot.
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Dinh, N., Goberna, M.A., López, M.A. et al. A Unifying Approach to Robust Convex Infinite Optimization Duality. J Optim Theory Appl 174, 650–685 (2017). https://doi.org/10.1007/s10957-017-1136-x
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DOI: https://doi.org/10.1007/s10957-017-1136-x
Keywords
- Robust convex optimization
- Lagrange duality
- Strong duality
- Robust strong duality
- Uniform robust strong duality
- Robust reverse strong duality