Abstract
AbstractA variety of approaches has been developed to deal with uncertain optimization problems. Often, they start with a given set of uncertainties and then try to minimize the influence of these uncertainties. The reverse view is to first set a budget for the price one is willing to pay and then find the most robust solution. In this article, we aim to unify these inverse approaches to robustness. We provide a general problem definition and a proof of the existence of its solution. We study properties of this solution such as closedness, convexity, and boundedness. We also provide a comparison with existing robustness concepts such as the stability radius, the resilience radius, and the robust feasibility radius. We show that the general definition unifies these approaches. We conclude with an example that demonstrates the flexibility of the introduced concept.
Funder
Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM
Publisher
Springer Science and Business Media LLC
Reference34 articles.
1. Ben-Tal A, Goryashko A, Guslitzer E, Nemirovski A (2004) Adjustable robust solutions of uncertain linear programs. Math Program 99(2):351–376
2. Ben-Tal A, El Ghaoui L, Nemirovski A (2009) Robust optimization. Princeton series in applied mathematics, vol 28. Princeton University Press, Princeton
3. Bertsimas D, Brown DB (2009) Constructing uncertainty sets for robust linear optimization. Oper Res 57(6):1483–1495
4. Bertsimas D, Sim M (2003) Robust discrete optimization and network flows. Math Program 98(1–3):49–71
5. Bertsimas D, Sim M (2004) The price of robustness. Oper Res 52(1):35–53
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献