DUALITY AND SUFFICIENCY IN MULTIOBJECTIVE FRACTIONAL PROGRAMMING WITH INVEXITY

  • Kim, Do-Sang (DEPT. OF APPLIED MATHEMATICS, PUKYONG NATIONAL UNIVERSITY) ;
  • Lee, Hyo-Jung (DEPT. OF APPLIED MATHEMATICS, PUKYONG NATIONAL UNIVERSITY)
  • Received : 2009.03.03
  • Accepted : 2009.04.19
  • Published : 2009.06.25

Abstract

In this paper, we introduce generalized multiobjective fractional programming problem with two kinds of inequality constraints. Kuhn-Tucker sufficient and necessary optimality conditions are given. We formulate a generalized multiobjective dual problem and establish weak and strong duality theorems for an efficient solution under generalized convexity conditions.

Acknowledgement

Supported by : Pukyong National University

References

  1. C.R. Bector, Duality in nonlinear fractional programming, Zeitschrift fur Ope. Res. 17 (1973), 183-193.
  2. V. Chankong and Y.Y. Haimes, Multiobjective Decision Making: Theory and Methodology, Elsevier Science Publishing Co. Inc., 1983.
  3. B.D. Craven and B. Mond, Fractional programming with invexity, in: Andrew Eberhard, Robin Hill, Daniel Ralph and Barney M. Glover(eds.), Progress in Optimization: Contributions from Australasia, Kluwer Academic Publishers, 1999, 79-89.
  4. M.A. Hanson, On sufficiency of the Kuhn-Tucker condition, J. Math. Anal. Appl. 80 (1981), 545-550. https://doi.org/10.1016/0022-247X(81)90123-2
  5. R. Jagannathan, Duality for nonlinear fractional programs, Z. Oper. Res. 17 (1973), 1-3.
  6. V. Jeyakumar and B. Mond, On generalized convex mathematical programming, J. Optl. Theo. Appl. 34(1992),43-53.
  7. Z.A. Khan and M.A. Hanson, On ratio invexity in mathematical programming, J. Math. Anal. Appl. 205 (1997), 330-336. https://doi.org/10.1006/jmaa.1997.5180
  8. P. Kanniappan, Necessary conditions for optimality of nondifferentiable convex multiobjective program, J. Opti. Theo. Appl. 40 (1983), 167-174. https://doi.org/10.1007/BF00933935
  9. D.S. Kim and S.J. Kim, Nonsmooth fractional programming with generalized ratio invexity, RIMS Kokyuroku 1365, April, pp.116-127, (2004).
  10. O.L. Mangasarian, Nonlinear programming, McGraw-Hill, New York, 1969.
  11. B. Mond and T.Weir, Duality for fractional programming with generalized convexity conditions, J. Inf. Optim. sci. 3 (1982), 105-124.
  12. B. Mond and T. Weir, Generalized convexity and higher order duality, in: S. Schaible, W.T. Ziemba(Eds.), Generalized Convexity in Optimization and Economics, Academic Press, New York, 1981, 263-280.
  13. S. Schaible, Duality in fractional programming : a unified approach, Oper. Res. 24 (1976), 452-461. https://doi.org/10.1287/opre.24.3.452
  14. S. Schaible, Fractional programming I : duality, Management Sci., 22 (1976), 858-867. https://doi.org/10.1287/mnsc.22.8.858
  15. P. Wolfe, A duality theorem for nonlinear programming, Quart. Appl. Math. 19 (1961), 239-244. https://doi.org/10.1090/qam/135625