Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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DUALITY THEOREM AND VECTOR SADDLE POINT THEOREM FOR ROBUST MULTIOBJECTIVE OPTIMIZATION PROBLEMS

  • Received : 2012.03.30
  • Published : 2013.07.31
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Abstract

In this paper, Mond-Weir type duality results for a uncertain multiobjective robust optimization problem are given under generalized invexity assumptions. Also, weak vector saddle-point theorems are obtained under convexity assumptions.

Keywords

Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

References

  1. A. Ben-Tal, L. E. Ghaoui, and A. Nemirovski, Robust Optimization, Princeton Series in Applied Mathematics, 2009.
  2. A. Ben-Tal and A. Nemirovski, Robust-optimization-methodology and applications, Math. Program. Ser B 92 (2002), no. 3, 453-480. https://doi.org/10.1007/s101070100286
  3. A. Ben-Tal and A. Nemirovski, Selected topics in robust convex optimization, Math. Program. Ser B 112 (2008), no. 1, 125-158.
  4. D. Bertsimas and D. Brown, Constructing uncertainty sets for robust linear optimization, Oper. Res. 57 (2009), no. 6, 1483-1495. https://doi.org/10.1287/opre.1080.0646
  5. D. Bertsimas, D. Pachamanova, and M. Sim, Robust linear optimization under general norms, Oper. Res. Lett. 32 (2004), no. 6, 510-516. https://doi.org/10.1016/j.orl.2003.12.007
  6. V. Jeyakumar, G. Li, and G. M. Lee, A robust von Neumann minimax theorem for zero-sum games under bounded payoff uncertainty, Oper. Res. Lett. 39 (2011), no. 2, 109-114. https://doi.org/10.1016/j.orl.2011.02.007
  7. V. Jeyakumar, G. Li, and G. M. Lee, Robust duality for generalized convex programming problems under data uncertainty, Nonlinear Anal. 75 (2012), no. 3, 1362-1373. https://doi.org/10.1016/j.na.2011.04.006
  8. M. H. Kim, Robust duality for generalized invex programming problems, submitted.
  9. D. Kuroiwa and G. M. Lee, On robust multiobjective optimization, submitted.

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