Abstract
AbstractPareto efficiency for robust linear programs was introduced by Iancu and Trichakis in [Manage Sci 60(1):130–147, 9]. We generalize their approach and theoretical results to robust optimization problems in Euclidean spaces with affine uncertainty. Additionally, we demonstrate the value of this approach in an exemplary manner in the area of robust semidefinite programming (SDP). In particular, we prove that computing a Pareto robustly optimal solution for a robust SDP is tractable and illustrate the benefit of such solutions at the example of the maximal eigenvalue problem. Furthermore, we modify the famous algorithm of Goemans and Williamson [Assoc Comput Mach 42(6):1115–1145, 8] in order to compute cuts for the robust max-cut problem that yield an improved approximation guarantee in non-worst-case scenarios.
Funder
Deutsche Forschungsgemeinschaft
HORIZON EUROPE Marie Sklodowska-Curie Actions
Friedrich-Alexander-Universität Erlangen-Nürnberg
Publisher
Springer Science and Business Media LLC
Subject
Control and Optimization,Business, Management and Accounting (miscellaneous)
Reference18 articles.
1. Ben-Tal, A., Nemirovski, A.: Robust convex optimization. In: Math. Oper. Res. 23(4) , 769–805. https://doi.org/10.1287/moor.23.4.769 (1998)
2. Ben-Tal, A., den Hertog, D., Vial, J.-P.: Deriving robust counterparts of nonlinear uncertain inequalities. In: Math. Program. Ser. A 149(1–2), 265–299. https://doi.org/10.1007/s10107-014-0750-8 (2015)
3. Bertsimas, D., Ten Eikelder, S., den Hertog, D., Trichakis, N.: Pareto Adaptive Robust Optimality via a Fourier-Motzkin Elimination Lens (2020)
4. Bilu, Y., Linial, N.: Are stable instances easy? Combin. Probab. Comput. 21(5), 643–660. (2012) https://doi.org/10.1017/S0963548312000193
5. Buchheim, C., Kurtz, J.: Robust combinatorial optimization under convex and discrete cost uncertainty. In: EURO J. Comput. Optim. 6(3), 211–238 (2018). https://doi.org/10.1007/s13675-018-0103-0
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