East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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ON SUFFICIENCY AND DUALITY FOR ROBUST OPTIMIZATION PROBLEMS INVOLVING (V, ρ)-INVEX FUNCTIONS

  • Kim, Moon Hee (Department of Refrigeration Engineering, Tongmyong University) ;
  • Kim, Gwi Soo (Department of Applied Mathematics, Pukyung National University)
  • Received : 2016.03.17
  • Accepted : 2016.12.26
  • Published : 2017.05.31
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Abstract

In this paper, we formulate a sufficient optimality theorem for the robust optimization problem (UP) under (V, ${\rho}$)-invexity assumption. Moreover, we formulate a Mond-Weir type dual problem for the robust optimization problem (UP) and show that the weak and strong duality hold between the primal problems and the dual problems.

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References

  1. D. Bertsimas, D. Brown, Constructing uncertainty sets for robust linear optimization, Oper. Res. 57(2009), 1483-1495. https://doi.org/10.1287/opre.1080.0646
  2. A. Ben-Tal, A. Nemirovski, Robust-optimization-methodology and applications, Math. Program., Ser B 92(2002), 453-480. https://doi.org/10.1007/s101070100286
  3. A. Ben-Tal, A. Nemirovski, A selected topics in robust convex optimization, Math. Program., Ser B 112(2008), 125-158.
  4. D. Bertsimas, D. Pachamanova, M. Sim, Robust linear optimization under general norms, Oper. Res. Lett. 32(2004), 510-516. https://doi.org/10.1016/j.orl.2003.12.007
  5. A. Ben-Tal, L.E. Ghaoui, A. Nemirovski, Robust optimization, Princeton Series in Applied Mathematics, 2009.
  6. V. Jeyakumar, G. Li, G. M. Lee, A robust von Neumann minimax theorem for zero-sum games under bounded payoff uncertainty, Oper. Res. Lett. 39(2011), 109-114. https://doi.org/10.1016/j.orl.2011.02.007
  7. H. Kuk, G. M. Lee and D. S. Kim, Nonsmooth multiobjective programs with ($V,\;{\rho}$)-invexity, Indian Journal of Pure and Applied Mathematics 29 (1998), 405-412.
  8. G.M. Lee and M.H. Kim, On duality theorems for robust optimization problems, J. Chungcheong Math. Soc. 26(2013), 723-733. https://doi.org/10.14403/jcms.2013.26.4.723