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2014 | OriginalPaper | Buchkapitel

A New Theoretical Framework for Robust Optimization Under Multi-Band Uncertainty

verfasst von : Christina Büsing, Fabio D’Andreagiovanni

Erschienen in: Operations Research Proceedings 2012

Verlag: Springer International Publishing

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Abstract

We provide an overview of our main results about studying Linear Programming Problems whose coefficient matrix is subject to uncertainty and the uncertainty is modeled through a multi-band set. Such an uncertainty set generalizes the classical one proposed by Bertsimas and Sim [3] and is particularly suitable in the common case of arbitrary non-symmetric distributions of the parameters. Our investigations were inspired by practical needs of our industrial partner in ongoing projects with focus on the design of robust telecommunications networks.

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Literatur
1.
Zurück zum Zitat Ben-Tal, A., El Ghaoui, L., Nemirovski, A.: Robust Optimization. Springer, Heidelberg (2009) Ben-Tal, A., El Ghaoui, L., Nemirovski, A.: Robust Optimization. Springer, Heidelberg (2009)
2.
Zurück zum Zitat Bertsimas, D., Brown, D., Caramanis, C.: Theory and applications of robust optimization. SIAM Rev. 53(3), 464–501 (2011)CrossRef Bertsimas, D., Brown, D., Caramanis, C.: Theory and applications of robust optimization. SIAM Rev. 53(3), 464–501 (2011)CrossRef
3.
Zurück zum Zitat Bertsimas, D., Sim, M.: The price of robustness. Oper. Res. 52(1), 35–53 (2004)CrossRef Bertsimas, D., Sim, M.: The price of robustness. Oper. Res. 52(1), 35–53 (2004)CrossRef
4.
Zurück zum Zitat Bienstock, D.: Histogram models for robust portfolio optimization. J. Comp. Finance 11(1), 1–64 (2007) Bienstock, D.: Histogram models for robust portfolio optimization. J. Comp. Finance 11(1), 1–64 (2007)
5.
Zurück zum Zitat Bley, A., D’Andreagiovanni, F., Hanemann, A.: Robustness in Communication Networks: Scenarios and Mathematical Approaches. In: Proc. of the ITG Symposium on Photonic Networks 2011, pp. 10–13. VDE Verlag, Berlin (2011) Bley, A., D’Andreagiovanni, F., Hanemann, A.: Robustness in Communication Networks: Scenarios and Mathematical Approaches. In: Proc. of the ITG Symposium on Photonic Networks 2011, pp. 10–13. VDE Verlag, Berlin (2011)
6.
Zurück zum Zitat Büsing, C.: Recoverable Robustness in Combinatorial Optimization. Ph.D. Thesis, Technische Universität Berlin, Berlin (2011) Büsing, C.: Recoverable Robustness in Combinatorial Optimization. Ph.D. Thesis, Technische Universität Berlin, Berlin (2011)
7.
Zurück zum Zitat Büsing, C., D’Andreagiovanni, F.: New Results about Multi-band Uncertainty in Robust Optimization. In: Klasing, R. (ed.) Experimental Algorithms - SEA 2012, LNCS, vol. 7276, pp. 63–74. Springer, Heidelberg (2012) Büsing, C., D’Andreagiovanni, F.: New Results about Multi-band Uncertainty in Robust Optimization. In: Klasing, R. (ed.) Experimental Algorithms - SEA 2012, LNCS, vol. 7276, pp. 63–74. Springer, Heidelberg (2012)
8.
Zurück zum Zitat Büsing, C., D’Andreagiovanni, F.: Robust Optimization under Multi-band Uncertainty. Submitted for publication (2012) Büsing, C., D’Andreagiovanni, F.: Robust Optimization under Multi-band Uncertainty. Submitted for publication (2012)
10.
Zurück zum Zitat D’Andreagiovanni, F., Mannino, C., Sassano, A.: GUB covers and power-indexed formulations for wireless network design. Management Sci. (2012). doi:10.1287/mnsc.1120.1571 D’Andreagiovanni, F., Mannino, C., Sassano, A.: GUB covers and power-indexed formulations for wireless network design. Management Sci. (2012). doi:10.​1287/​mnsc.​1120.​1571
11.
Zurück zum Zitat Dantzig, G.: Linear programming under uncertainty. Manage. Sci. 1, 197–206 (1955)CrossRef Dantzig, G.: Linear programming under uncertainty. Manage. Sci. 1, 197–206 (1955)CrossRef
12.
Zurück zum Zitat Fischetti, M., Monaci, M.: Cutting plane versus compact formulations for uncertain (integer) linear programs. Math. Prog. C 4(3), 239–273 (2012)CrossRef Fischetti, M., Monaci, M.: Cutting plane versus compact formulations for uncertain (integer) linear programs. Math. Prog. C 4(3), 239–273 (2012)CrossRef
13.
Zurück zum Zitat International Telecommunication Union (ITU): Terrestrial and satellite digital sound broadcasting to vehicular, portable and fixed receivers in the VHF/UHF bands (2002) International Telecommunication Union (ITU): Terrestrial and satellite digital sound broadcasting to vehicular, portable and fixed receivers in the VHF/UHF bands (2002)
14.
Zurück zum Zitat Koster, A.M.C.A., Kutschka, M., Raack, C.: Robust Network Design: Formulations, Valid Inequalities, and Computations. ZIB Tech. Rep. 11–34, ZIB Berlin, Berlin, Germany (2011) Koster, A.M.C.A., Kutschka, M., Raack, C.: Robust Network Design: Formulations, Valid Inequalities, and Computations. ZIB Tech. Rep. 11–34, ZIB Berlin, Berlin, Germany (2011)
15.
Zurück zum Zitat Mannino, C., Rossi, F., Smriglio, S.: The network packing problem in terrestrial broadcasting. Oper. Res. 54(6), 611–626 (2006)CrossRef Mannino, C., Rossi, F., Smriglio, S.: The network packing problem in terrestrial broadcasting. Oper. Res. 54(6), 611–626 (2006)CrossRef
16.
Zurück zum Zitat Nemhauser, G., Wolsey, L.: Integer and Combinatorial Optimization. Wiley, Hoboken (1988) Nemhauser, G., Wolsey, L.: Integer and Combinatorial Optimization. Wiley, Hoboken (1988)
17.
Zurück zum Zitat Rappaport, T.S.: Wireless Communications: Principles and Practice, 2nd edn. Prentice Hall, Upper Saddle River (2001) Rappaport, T.S.: Wireless Communications: Principles and Practice, 2nd edn. Prentice Hall, Upper Saddle River (2001)
Metadaten
Titel
A New Theoretical Framework for Robust Optimization Under Multi-Band Uncertainty
verfasst von
Christina Büsing
Fabio D’Andreagiovanni
Copyright-Jahr
2014
DOI
https://doi.org/10.1007/978-3-319-00795-3_17