On second- order symmetric duality for a class of multiobjective fractional programming problem


  • Deo Brat Ojha




$(F, \rho)$-(pseudo/quasi)-convexity/univexity, multiobjective programming, duality theorem


This article is concerned with a pair of second-order symmetric duals in the context of non-differentiable multiobjective fractional programming problems. We establish the weak and strong duality theorems for the new pair of dual models. Discussion on some special cases shows that results in this paper extend previous work in this area.


B. Agezzaf, Second-order necessary and sufficient conditions of Kuhn-Tucker type in multiobjective optimization problems, in Twelfth International Conference On Multiobjective Criteria Decision Making, Fernuniversitat Hangen, Hangen Germany, 1995.

B. Agezzaf and M. Hachimi, Second order optimality conditions in multiobjective optimization problems, J. Optim. Theory Appl., 102 (1999), 37--50.

C. R. Bector and S. Chandra, Generalized bonvexity and higher order duality for fractional programming, Opsearch, 24 (1987), 143--154.

S. Chandra and G. Abha, Symmetric duality in multiobjective programs :some remarks on recent results, Eur. J. Oper. Res., 124(2000), 651--654.

S. Chandra, B. D. Craven and B. Mond, Symmetric dual fractional programming, Z. Oper. Res., 29(1985), 59--64.

S. Chandra, B. D. Craven and B. Mond, Generalized concavity and duality with a square root term,

Optimization, 16(1985), 654--662.

S. Chandra and M. V. D. Prasad, Symmetric duality in multiobjective programming, J. Austral. Math. Soc. Ser. B, 35(1993), 198--206.

R. W. Cottle, Symmetric dual quadratic programs, Quart. Appl. Math., 21(1963), 237--243.

B. D. Craven, textit{Lagrangian conditions and quasiduality, Bull. Austral. Math. Soc., 16(1977), 325--339.

G. G. Dantzig, E. Eisenberg and R. W. Cottle, Symmetric dual nonlinear programs, Pacific J. Math., 15(1965), 809--812.

W. S. Dorn, textit{A symmetric dual theorem for quadratic programs, J. Oper. Res. Soc. Japan, 2(1960), 93--97.

T. R. Gulati and I. Ahmad, Second order symmetric duality for nonlinear mixed integer programs, European J. Oper. Res.,101(1997), 122-129.

A. M. Geoffrion, Proper efficiencyand the theory of vector optimization, J. Math. Anal. Appl., 22(1968), 613--630.

S. H. Hou and X. M. Yang, On second -order symmetric duality in nondifferentiable programming, J. Math. Anal. Appl., 255(2001), 491--498.

I. Hussain and G. Abha, Nondifferentiable Symmetric Duality in Fractional Programming, Opsearch, 2000.

M. A. Hanson, On sufficiency of the Kuhn - Tucker conditions, J. Math. Anal. Appl., 80(1981), 545--550.

R. N. Kaul and S. Kaur, Optimality criteria in nonlinear programming involving nonconvex functions, J.Math. Anal. Appl., 105(1985), 104-112.

O. L. Mangasarian, Second and higher order duality in nonlinear programming, J. Math. Anal. Appl., 5(1975), 607--620.

B. Mond, A symmetric dual theory for nonlinear programs, Quart. Appl. Math., 23(1965), 265--269.

B. Mond and I. Hussain and M. V. D. Prasad, Duality for a class of nondifferentiable multi- objective programs, Util. Math., 39(1991), 3--19.

B. Mond and M. Schechter, Nondifferentiable symmetric duality, Bull. Austral. Math. Soc., 53(1996), 177--188.

B. Mond, S. Chandra and M. V. D. Prasad, Symmetric dual nondifferentiable fractional programs, Indian J. Manag. Syst., 13 (1987), 1--10.

M. Schechter, More on subgradient duality, J. Math. Anal. Appl., 71(1979),251--262.

I. M. -Minasian Stancu, Fractional programming : Theory, Methods and Applications, in : Mathematics and its Applications,Vol.409, Kluwer Academic, Dordrecht, 1997 .

S. Wang, Second order necessary and sufficient conditions in multiobjective programming, Numeri. Funct. Anal. Optim., 12(1991), 237--252.

T. Wier, Symmetric dual multiobjective fractional programming, J. Austral. Math. Soc. Ser. A, 50(1991), 67--74.

T. Weir and B. Mond, Symmetric and self duality in multiobjective programming, Asia Pacific J. Oper. Res., 5(1988), 124--133.

X. M. Yang, S. Y. Wang and X. T. Deng, Symmetric duality for a class of multiobjective fractional programming problems, J. Math. Anal. Appl., 274(2002), 279--295.




How to Cite

Ojha, D. B. (2012). On second- order symmetric duality for a class of multiobjective fractional programming problem. Tamkang Journal of Mathematics, 43(2), 267-279. https://doi.org/10.5556/j.tkjm.43.2012.1183