Optimality and duality for a class of nondifferentiable minimax fractional programming problems

Authors

  • Antoan Bătătorescu University of Bucharest, Bucharest, Romania
  • Miruna Beldiman Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, Bucharest, Romania
  • Iulian Antonescu 'Mircea cel Bătrân' Naval Academy, Constanţa, Romania
  • Roxana Ciumara Academy of Economic Studies, Bucharest, Romania

DOI:

https://doi.org/10.2298/YJOR0901049B

Keywords:

Fractional programming, generalized invexity, optimality conditions, duality

Abstract

Necessary and sufficient optimality conditions are established for a class of nondifferentiable minimax fractional programming problems with square root terms. Subsequently, we apply the optimality conditions to formulate a parametric dual problem and we prove some duality results.

References

Bector, C.R., Bhatia, B.L. (1985) Sufficient optimality conditions and duality for a minmax problem. Utilitas Math, 27 229-247

Chandra, S., Kumar, V. (1995) Duality in fractional minimax programming. Journal of the Australian Mathematical Society, 58(3): 376

Lai, H.C., Liu, J.C., Tanaka, K. (1999) Necessary and sufficient conditions for minimax fractional programming. Journal of Mathematical Analysis and Applications, 230(2): 311

Liu, J.C. (1996) Optimality and duality for generalized fractional programming involving nonsmooth (F, ρ)-convex functions. Computers & Mathematics with Applications, 32(2): 91

Liu, J.C., Wu, C.S. (1998) On minimax fractional optimality conditions with (F, ρ) - convexity. Journal of Mathematical Analysis and Applications, 219(1): 36

Schmitendorf, W.E. (1977) Necessary conditions and sufficient conditions for static minmax problems. Journal of Mathematical Analysis and Applications, 57(3): 683

Singh, C. (1984) Optimality conditions for fractional minmax programming. Journal of Mathematical Analysis and Applications, 100(2): 409

Sinha, S.M. (1966) A extension of a theorem of supports of a convex function. Management Sci, 16, 409-415

Yadev, S.R., Mukherjee, R.N. (1990) Duality for fractional minimax programming problems. Journal of the Australian Mathematical Society Series B Applied Mathematics, 31(4): 484

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Published

2009-03-01

Issue

Vol. 19 No. 1 (2009)

Section

Research Articles

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