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Tytuł artykułu

Fractional programming with (p,r)-invexity

Autorzy
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The notion of (p, r)-invexity for a vector function is introduced and discussed its application to a class of fractional problems. Parametric and non-parametric necessary and sufficient optimality conditions and duality results for a generalized fractional programming are obtained under an appropriate (p,r)-invexity assumption on involving functions.
Rocznik
Strony
5--29
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
autor
  • Faculty of Mathematics, University of Łódź
Bibliografia
  • [1] T. Antczak, (p, r)-Invex Sets and Functions, preprint (1998), University of Lódz
  • [2] --, r-Invexity in Mathematical Programming, to be published
  • [3] M. Avriel, r-convex functions, Mathematical Programming 2 (1972), pp. 309-323
  • [4] M. S. Bazaraa, H. D. Sherali, C. M. Shetty, Nonlinear programming: theory and algorithms, John Wiley and Sons, New York (1991)
  • [5] C. R. Bector, S. Chandra, M. K. Bector, Generalized fractional programming duality: a parametric approach, Journal of Optimization Theory and Applications, Vol.60 (1989), pp. 243-260
  • [6] A. Ben-Israel, B. Mond, What is invexity?, Journal of Australian Mathematical Society Ser.B 28 (1986), pp. 1-9
  • [7] A. Cambini, E. Castagnoli, L. Martein, P. Mazzoleni,. S. Schaible (eds.), Generalized convexity and fractional programming with economic applications, Proc. International Workshop on Generalized Convexity, Fractional Programming and Economic Applications, Pisa, Italy: Lecture Notes in Econ. Math. Systems, 345 (1988), Springer Berlin, 1990
  • [8] S. Chandra, V. Kumar, Duality in fractional minimax progmmming, Journal of Australian Mathematical Society Ser.A 58 (1995), pp. 376-386
  • [9] S. Chandra, B. D. Craven, B. Mond, Generalized fractional programming duality: a ratio game approach, Journal of Australian Mathematical Society Ser.B 28 (1986), pp. 170-180
  • [10] J. P. Crouzeix, J. A. Ferland, S. Schaible, An algorithm for generalized fractional programs, Jour'nal of Optimization Theory and Applications: Vol.47 (1985), pp. 35-49
  • [11] T. R. Gulati, I. Ahmad, Efficiency and duality in multiobjective Jmctional programming, Opserch 32 (1990), pp. 31-43
  • [12] A. M. Hanson, On sufficiency of the Kuhn-Tucker conditions, Journal of Mathematical Analysis and Applications 80 (1981), pp. 545-550
  • [13] R. Jagannathan, S. Schiable, Duality in genemlized fractional progmmming via Farkas'lemma, Journal of Optimization Theory and Applications, Vol.41 (1983), pp. 417-424
  • [14] O. L. Mangasarian, Nonlinear programming, McGraw-Hill, New York (1969)
  • [15] B. Mond, T. Weir, Generalized concavity and duality, in "Generalized Concavity in Optimization and economics" (S. Schaible and W.T. Ziemba, Eds.) pp. 263-279, Academic Press, New York (1981)
  • [16] N. G. Rueda, M. A. Hanson, Optimality criteria in mathematical programming involving generalized invexity, Journal of Mathematical Analysis and Applications 130 (1988), pp. 375-385
  • [17] S. Schiable, T. Ibaraki, Practional Programming, European Journal of Operational Research 12 (1983), pp. 325-338
  • [18] C. Singh, N. Rueda, Generalized fractional programming: Optimality and duality theory, Journal of Optimization Theory and Applications: Vol.66 (1990), pp. 149-159
  • [19] J. Von Neumann, A model of generał economic equilibrium, Rev.Econ.Studies, 13 (1945), pp. 1-9
  • [20] T. Weir, A dual for multiobjective fractional programming, Opserch, 22 (1986), pp. 241-247
  • [21] P. Wolfe, A duality theorem for nonlinear programming, Quarterly of Applied Mathematics, Vol.19 (1961), pp. 239-244
  • [22] G. J. Zalmai, Optimality conditions and duality models for generalized fractional programming problems containing locally subdifferentiable and p-convex functions, Optimization Vol.32 (1995), pp. 95-124
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA3-0043-0020
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