DOI QR코드

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DUALITY THEOREM AND VECTOR SADDLE POINT THEOREM FOR ROBUST MULTIOBJECTIVE OPTIMIZATION PROBLEMS

  • Received : 2012.03.30
  • Published : 2013.07.31

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

robust multiobjective optimization;robust weakly efficient solution;necessary optimality theorem;Mond-Weir type robust duality

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.

Cited by

  1. Robust canonical duality theory for solving nonconvex programming problems under data uncertainty vol.84, pp.1, 2016, https://doi.org/10.1007/s00186-016-0539-z
  2. On nonsmooth robust multiobjective optimization under generalized convexity with applications to portfolio optimization 2017, https://doi.org/10.1016/j.ejor.2017.08.003
  3. Optimality Conditions and Duality for Robust Nonsmooth Multiobjective Optimization Problems with Constraints pp.1573-2878, 2018, https://doi.org/10.1007/s10957-018-1437-8
  4. On approximate solutions for nonsmooth robust multiobjective optimization problems pp.1029-4945, 2019, https://doi.org/10.1080/02331934.2019.1579212

Acknowledgement

Supported by : National Research Foundation of Korea(NRF)