论文信息 - Duality for fractional minimax programming problems

Duality for fractional minimax programming problems

Abstract Duality theory is discussed for fractional minimax programming problems. Two dual problems are proposed for the minimax fractional problem: minimize maxy∈Υf(x, y)/h(x, y), subject to g(x) ≤ 0. For each dual problem a duality theorm is established. Mainly these are generalisations of the results of Tanimoto [14] for minimax fractional programming problems. It is noteworthy here that these problems are intimately related to a class of nondifferentiable fractional programming problems.

R. N. Mukherjee | R. Mukherjee | Shri Ram Yadav | Shrishti Yadav

[1] G. A. Garreau,et al. Mathematical Programming and Control Theory , 1979, Mathematical Gazette.

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

[3] Chanchal Singh. Optimality conditions for fractional minmax programming , 1984 .

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

[5] S. Sinha. A Duality Theorem for Nonlinear Programming , 1966 .

[6] Murray Schechter,et al. A Subgradient Duality Theorem , 1977 .

[7] Siegfried Schaible,et al. Duality in generalized fractional programming via Farkas' lemma , 1983 .

[8] Olvi L. Mangasarian,et al. Nonlinear Programming , 1969 .

[9] Apex duality for constrained optimization , 1986, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[10] Hirotaka Nakayama,et al. Theory of Multiobjective Optimization , 1985 .

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

[12] Kenneth O. Kortanek,et al. Semi-Infinite Programming and Applications , 1983, ISMP.

[13] Bertram Mond. A class of nondifferentiable mathematical programming problems , 1974 .

[14] P. Wolfe. A duality theorem for non-linear programming , 1961 .