Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2014, Special Issue (2014), Article ID 209239, 7 pages.

Robust Linear Programming with Norm Uncertainty

Lei Wang and Hong Luo

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Abstract

We consider the linear programming problem with uncertainty set described by p , w -norm. We suggest that the robust counterpart of this problem is equivalent to a computationally convex optimization problem. We provide probabilistic guarantees on the feasibility of an optimal robust solution when the uncertain coefficients obey independent and identically distributed normal distributions.

Article information

Source
J. Appl. Math., Volume 2014, Special Issue (2014), Article ID 209239, 7 pages.

Dates
First available in Project Euclid: 1 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1412177567

Digital Object Identifier
doi:10.1155/2014/209239

Mathematical Reviews number (MathSciNet)
MR3212487

Citation

Wang, Lei; Luo, Hong. Robust Linear Programming with Norm Uncertainty. J. Appl. Math. 2014, Special Issue (2014), Article ID 209239, 7 pages. doi:10.1155/2014/209239. https://projecteuclid.org/euclid.jam/1412177567


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References

  • A. Soyster, “Convex programming with set-inclusive constraints and applications to in-exact linear programming,” Operation Research, vol. 21, no. 5, pp. 1154–1157, 1973.
  • A. Ben-Tal and A. Nemirovski, “Robust solutions of uncertain linear programs,” Operation Research Letters, vol. 25, no. 1, pp. 1–13, 1999.
  • A. Ben-Tal and A. Nemirovski, “Robust convex optimization,” Mathematics of Operations Research, vol. 23, no. 4, pp. 769–805, 1998.
  • L. El Ghaoui, F. Oustry, and H. Lebret, “Robust solutions to uncertain semidefinite programs,” SIAM Journal on Optimization, vol. 9, no. 1, pp. 33–52, 1999.
  • L. El Ghaoui and H. Lebret, “Robust solutions to least-squares problems with uncertain data,” SIAM Journal on Matrix Analysis and Applications, vol. 18, no. 4, pp. 1035–1064, 1997.
  • D. Bertsimas and M. Sim, “The price of robustness,” Operations Research, vol. 52, no. 1, pp. 35–53, 2004.
  • D. Bertsimas, D. Pachamanova, and M. Sim, “Robust linear optimization under general norms,” Operations Research Letters, vol. 32, no. 6, pp. 510–516, 2004.
  • A. Ben-Tal and A. Nemirovski, “Robust solutions of linear programming problems contaminated with uncertain data,” Mathematical Programming, vol. 88, no. 3, pp. 411–424, 2000.
  • A. Ben-Tal and A. Nemirovski, “Robust solutions of uncertain linear programs,” Operations Research Letters, vol. 25, no. 1, pp. 1–13, 1999.
  • A. Ben-Tal and A. Nemirovski, “Robust solutions of uncertain linear programs,” Operations Research Letters, vol. 25, no. 1, pp. 1–13, 1999.
  • C. Gregory, K. Darby-Dowman, and G. Mitra, “Robust optimization and portfolio selection: the cost of robustness,” European Journal of Operational Research, vol. 212, no. 2, pp. 417–428, 2011.
  • G. N. Iyengar, “Robust dynamic programming,” Mathematics of Operations Research, vol. 30, no. 2, pp. 257–280, 2005.
  • E. Erdo\vgan and G. Iyengar, “Ambiguous chance constrained problems and robust optimization,” Mathematical Programming, vol. 107, no. 1-2, pp. 37–61, 2006.
  • A.-L. Yan, G.-Y. Wang, and N.-H. Xiu, “Robust solutions of split feasibility problem with uncertain linear operator,” Journal of Industrial and Management Optimization, vol. 3, no. 4, pp. 749–761, 2007.
  • H.-M. Zhao, X.-Z. Xu, and N.-J. Huang, “Robust solutions of uncertain extended weighted steiner problems with applications,” Communications on Applied Nonlinear Analysis, vol. 16, no. 4, pp. 15–26, 2009. \endinput