Optimality Conditions and Duality in Nondifferentiable Minimax Fractional Programming with Generalized Convexity

We establish sufficient optimality conditions for a class of nondifferentiable minimax fractional programming problems involving (F, α, ρ, d)-convexity. Subsequently, we apply the optimality conditions to formulate two types of dual problems and prove appropriate duality theorems.

[1]  S. Chandra,et al.  Duality in fractional minimax programming , 1995, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

[2]  Panos M. Pardalos,et al.  Efficiency Conditions and Duality for a Class of Multiobjective Fractional Programming Problems , 2003, J. Glob. Optim..

[3]  Panos M. Pardalos,et al.  Optimality Conditions and Duality for a Class of Nonlinear Fractional Programming Problems , 2001 .

[4]  Shinji Tanimoto.  Duality for a class of nondifferentiable mathematical programming problems , 1981 .

[5]  Kensuke Tanaka,et al.  Necessary and sufficient conditions for minimax fractional programming , 1999 .

[6]  W. Schmitendorf.  Necessary conditions and sufficient conditions for static minmax problems , 1977 .

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

[8]  J. C. Lee,et al.  On duality theorems for a nondifferentiable minimax fractional programming , 2002 .

[9]  J. C Liu,et al.  On Minimax Fractional Optimality Conditions with Invexity , 1998 .

[10]  Zhi-an Liang,et al.  Optimality conditions and duality for a minimax fractional programming with generalized convexity , 2003 .

[11]  Kin Keung Lai,et al.  Nondifferentiable minimax fractional programming under generalized univexity , 2003 .

[12]  C. S Wu,et al.  On minimax fractional optimality conditions with (F, ρ)-convexity , 1998 .

[13]  Bernard Hanzon,et al.  REPORT RAPPORT , 2001 .

[14]  R. N. Mukherjee,et al.  Duality for fractional minimax programming problems , 1990, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

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