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2007 | 5 | 3 | 452-469
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Comparison between different duals in multiobjective fractional programming

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Języki publikacji
EN
Abstrakty
EN
The present paper is a continuation of [2] where we deal with the duality for a multiobjective fractional optimization problem. The basic idea in [2] consists in attaching an intermediate multiobjective convex optimization problem to the primal fractional problem, using an approach due to Dinkelbach ([6]), for which we construct then a dual problem expressed in terms of the conjugates of the functions involved. The weak, strong and converse duality statements for the intermediate problems allow us to give dual characterizations for the efficient solutions of the initial fractional problem. The aim of this paper is to compare the intermediate dual problem with other similar dual problems known from the literature. We completely establish the inclusion relations between the image sets of the duals as well as between the sets of maximal elements of the image sets.
Wydawca
Czasopismo
Rocznik
Tom
5
Numer
3
Strony
452-469
Opis fizyczny
Daty
wydano
2007-09-01
online
2007-09-01
Bibliografia
  • [1] C.R. Bector, S. Chandra and C. Singh: “Duality on multiobjective fractional programming/rd, In: Lecture Notes in Economics and Mathematical Systems, Vol. 345, Springer Verlag, Berlin, 1990, pp. 232–241.
  • [2] R.I. Boţ, R. Chares and G. Wanka: “Duality for multiobjective fractional programming problems/rd, Nonlinear Anal. Forum, Vol. 11, (2006), pp. 185–201.
  • [3] R.I. Boţ and G. Wanka: “An analysis of some dual problems in multiobjective optimization (I)/rd, Optimization, Vol. 53, (2004), pp. 281–300. http://dx.doi.org/10.1080/02331930410001715514
  • [4] R.I. Boţ and G. Wanka: “An analysis of some dual problems in multiobjective optimization (II)/rd, Optimization, Vol. 53, (2004), pp. 301–324. http://dx.doi.org/10.1080/02331930410001715523
  • [5] S. Chandra, B.D. Craven and B. Mond: “Multiobjective fractional programming duality. A Lagrangian approach/rd, Optimization, Vol. 22, (1991), pp. 549–556.
  • [6] W. Dinkelbach: “On nonlinear fractional programming/rd, Management Science, Vol. 13, (1967), pp. 492–497.
  • [7] A.M Geoffrion: “Proper efficiency and the theory of vector maximization/rd, J. Math. Anal. Appl., Vol. 22, (1968), pp. 618–630. http://dx.doi.org/10.1016/0022-247X(68)90201-1
  • [8] J. Jahn: “Duality in vector optimization/rd, Math. Program., Vol. 25, (1983), pp. 343–353. http://dx.doi.org/10.1007/BF02594784
  • [9] R.N. Kaul and V. Lyall: “A note on nonlinear fractional vector maximization/rd, OPSearch, Vol. 26, (1989), pp. 108–121.
  • [10] H. Nakayama: “Geometric consideration of duality in vector optimization/rd, J. Optimiz. Theory App., Vol. 44, (1984), pp. 625–655. http://dx.doi.org/10.1007/BF00938399
  • [11] E. Ohlendorf and Ch. Tammer: “Multicriteria fractional programming - an approach by means of conjugate functions/rd, OR Spektrum, Vol. 16, (1994), pp. 249–254. http://dx.doi.org/10.1007/BF01720317
  • [12] R.T. Rockafellar: Convex analysis, Princeton University Press, 1970.
  • [13] G. Wanka and R.I. Boţ: “A new duality approach for multiobjective convex optimization problems/rd, J. Nonlinear and Convex Anal., Vol. 3, (2002), pp. 41–57.
  • [14] G. Wanka and R.I. Boţ: “On the relations between different dual problems in convex mathematical programming/rd, In: P. Chamoni and R. Leisten and A. Martin and J. Minnemann and A. Stadler (Eds.), Operations Research Proceedings 2001, Springer-Verlag, Berlin, 2002, pp. 255–265.
  • [15] T. Weir: “Proper efficiency and duality for vector valued optimization problems/rd, J. Aust. Math. Soc., Vol. 43, (1987), pp. 21–34
  • [16] T. Weir and B. Mond: “Generalised convexity and duality in multiple objective programming”, Bull. Aust. Math. Soc., Vol. 39, (1989), pp. 287–299. http://dx.doi.org/10.1017/S000497270000277X
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-007-0019-z
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