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  • The Journal of the Australian Mathematical Society. Series B. Applied Mathematics, Volume 31, Issue 4
  • April 1990, pp. 484-492

Duality for fractional minimax programming problems

  • Shri Ram Yadav (a1) and R. N. Mukherjee (a1)
  • DOI: http://dx.doi.org/10.1017/S0334270000006809
  • Published online: 01 February 2009
Abstract
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.

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[2] B. D. Craven , Mathematical Programming and Control Theory (Chapman and Hall, London, 1978).

[3] R. J. Duffin , “Numerical estimation of optima by use of dual inequalities”, in Semi-infinite programming and applications (eds. A. V. Fiacco and K. O. Kortanek ), (Springer-Verlag, Berlin, 1983) 118127.

[7] B. Mond , “A class of nondifferentiable mathematical programming problems, J. of Math. Anal. and Appl. 46 (1974) 169174.

[9] R. Rockafellar , Convex analysis (Princeton University, press, Princeton, New Jersey, 1970).

[11] M. Schechter , “A subgradient duality theorem”, J. of Math. Anal. and Appl. 61 (1977) 850855.

[12] W. E. Schmitendorf , “Necessary conditions and sufficient conditions for static minimax problems”, J. of Math. Anal. and Appl. 57 (1977) 683”693.

[13] C. Singh , “Optimality conditions for fractional minimax programming, J. of Math. Anal. and Appl. 100 (1984) 409415.

[14] S. Tanimoto , “Duality for a class of nondifferentiable mathematical programming problems”, J. of Math. Anal. and Appl. 79 (1981) 283294.

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