DOI QR코드

DOI QR Code

ON OPTIMALITY AND DUALITY FOR GENERALIZED FRACTIONAL ROBUST OPTIMIZATION PROBLEMS

  • KIM, MOON HEE (DEPARTMENT OF REFRIGERATION ENGINEERING, TONGMYONG UNIVERSITY) ;
  • KIM, GWI SOO (DEPARTMENT OF APPLIED MATHEMATICS, PUKYUNG NATIONAL UNIVERSITY)
  • Received : 2015.04.27
  • Accepted : 2015.09.25
  • Published : 2015.09.30

Abstract

In this paper, we consider a generalized fractional robust optimization problem (FP). Establishing a nonfractional optimization problem (NFP) equivalent to (FP), we establish necessary optimality conditions and duality results.

Keywords

References

  1. D. Bertsimas, D. Brown, Constructing uncertainty sets for robust linear optimization, Opera. 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. 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
  6. 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
  7. M. H. Kim and Gwi Soo Kim, Optimality Conditions and Duality in Fractional Robust Optimization Problems, East Asian Math. J. 31(2015), 345-349. https://doi.org/10.7858/eamj.2015.025
  8. D. Kuroiwa and G. M. Lee, On robust multiobjective optimization, Vietnam J. Math. 40(2012), 305-317.
  9. 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
  10. 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.