Optimality and duality for multiobjective fractional programming involving nonsmooth($si:F$esi:ρ)–convex functions

We establish the Kuhn-Tucker necessary and sufficient conditions for an efficient optimum of multiobjective fractional programming problems containing ($si:F$esi:ρ)-convex functions. Bector type dual for multiobjective fractional programming problem is introduced and certain duality results have been derived in the framework of ($si:F$esi:ρ)-convex functions.

[1]  T. Weir A Dual For A Multiple Objective Fractional Programming Problem , 1986 .

[2]  Vaithilingam Jeyakumar,et al.  On generalised convex mathematical programming , 1992, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[3]  Davinder Bhatia,et al.  On Multi-Objective Fractional Duality for Hanson-Mond Classes of Functions , 1993 .

[4]  Â. J. Vial,et al.  Strong Convexity of Sets and Functions , 1982 .

[5]  M. A. Hanson On sufficiency of the Kuhn-Tucker conditions , 1981 .

[6]  B. M. Glover,et al.  Invex functions and duality , 1985, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

[7]  L. N. Das,et al.  Pseudo-invexity and symmetric duality in nonlinar programming , 1994 .

[8]  J. Ponstein,et al.  Seven kinds of convexity , 1967 .

[9]  Vasile Preda,et al.  On efficiency and duality for multiobjective programs , 1992 .

[10]  T. R. Gulati,et al.  Sufficiency and Duality in Multiobjective Programming Involving Generalized F-Convex Functions , 1994 .

[11]  Surjeet Kaur,et al.  Optimality Criteria in Nonlinear Programming Involving Nonconvex Functions , 1985 .

[12]  Jean-Philippe Vial,et al.  Strong and Weak Convexity of Sets and Functions , 1983, Math. Oper. Res..

[13]  Duality for minmax programming involving V-invex functions , 1994 .

[14]  C. R. Bector,et al.  Optimality conditions and duality in subdifferentiable multiobjective fractional programming , 1993 .

[15]  T. Weir,et al.  A duality theorem for a multiple objective fractional optimization problem , 1986, Bulletin of the Australian Mathematical Society.

[16]  S. Suneja,et al.  Preinvexity in Multiobjective Fractional Programming , 1992 .

[17]  C. R. Bector,et al.  Generalized fractional programming duality: A parametric approach , 1989 .

[18]  Gue Myung Lee Nonsmooth Invexity in Multiobjective Programming , 1994 .

[19]  Hanson's duality theorem in nonsmooth programming , 1994 .

[20]  Richard R. Egudo Multiobjective fractional duality , 1988, Bulletin of the Australian Mathematical Society.

[21]  Jean-Baptiste Hiriart-Urruty,et al.  On optimality conditions in nondifferentiable programming , 1978, Math. Program..

[22]  J. C. Liu Optimality and duality for multiobjective fractional programming involving nonsmooth pseudoinvex functions , 1996 .

[23]  S. Schaible,et al.  An algorithm for generalized fractional programs , 1985 .

[24]  B. Mond,et al.  Generalized fractional programming duablity: a ratio game approach , 1986, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[25]  Vasile Preda,et al.  On Sufficiency and Duality for Generalized Quasiconvex Programs , 1994 .

[26]  Chanchal Singh,et al.  A class of multiple-criteria fractional programming problems , 1986 .

[27]  R. Kaul,et al.  Optimality criteria and duality in multiple-objective optimization involving generalized invexity , 1994 .

[28]  P. Jain,et al.  Generalized (F, ρ)-convexity and duality for non smooth multi-objective programs , 1994 .

[29]  On generalized pseudoconvex functions , 1989 .

[30]  M. A. Hanson,et al.  Multiobjective duality with invexity , 1987 .

[31]  Toshihide Ibaraki,et al.  Parametric approaches to fractional programs , 1983, Math. Program..

[32]  Jochen Werner Duality in Generalized Fractional Programming , 1988 .

[33]  G. J. Zalmai Optimality conditions and duality models for generalized fractional programming problems containing locally subdifferentiable and ρ:-convex functions , 1995 .