East Asian mathematical journal

  • 제31권3호
  • /
  • Pages.345-349
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  • 2015
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  • 1226-6973(pISSN)
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  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
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OPTIMALITY CONDITIONS AND DUALITY IN FRACTIONAL ROBUST OPTIMIZATION PROBLEMS

  • Kim, Moon Hee (Department of Refrigeration Engineering, Tongmyong University) ;
  • Kim, Gwi Soo (Department of Applied Mathematics, Pukyung National University)
  • 투고 : 2014.10.15
  • 심사 : 2015.03.30
  • 발행 : 2015.05.31
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초록

In this paper, we consider a fractional robust optimization problem (FP) and give necessary optimality theorems for (FP). Establishing a nonfractional optimization problem (NFP) equivalent to (FP), we formulate a Mond-Weir type dual problem for (FP) and prove duality theorems for (FP).

키워드

참고문헌

  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. 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
  4. V. Jeyakumar, G. Li, G. M. Lee, Robust duality for generalized convex programming problems under data uncertainty, Nonlinear Anal. 75(2012), 1362-1373. https://doi.org/10.1016/j.na.2011.04.006
  5. M. H. Kim, Robust duality for generalized invex programming problems, Commun. Korean Math. Soc. 28(2013), 419-423. https://doi.org/10.4134/CKMS.2013.28.2.419
  6. D. Kuroiwa and G. M. Lee, On robust multiobjective optimization, Vietnam J. Math. 40(2012), 305-317.
  7. G. M. Lee and M. H. Kim, On duality theorems for robust optimization problems, J. Chungcheong Math. Soc. 26(2013), 723-734. https://doi.org/10.14403/jcms.2013.26.4.723
  8. G. M. Lee and D. S. Kim, Duality theorems for fractional multiobjective minimization problems, Proceedings of the 1st Workshop in Applied Mathematics 1 (1993), 245-256.

피인용 문헌

  1. ON OPTIMALITY AND DUALITY FOR GENERALIZED FRACTIONAL ROBUST OPTIMIZATION PROBLEMS vol.31, pp.5, 2015, https://doi.org/10.7858/eamj.2015.054
  2. ON SUFFICIENCY AND DUALITY FOR FRACTIONAL ROBUST OPTIMIZATION PROBLEMS INVOLVING (V, ��)-INVEX FUNCTION vol.32, pp.5, 2016, https://doi.org/10.7858/eamj.2016.043