Abstract
In this paper, we have pointed out that the proofs of the Theorems 3.1 and 3.3 in the recent paper (Sonali et al. in Ann Oper Res 244:603–617, 2016) are erroneous. A modified dual to the second order minimax fractional programming problem has been formulated and the rectified proofs of these results under generalized B-(p,r)-invexity have been established.
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Reference
Sonali, Kailey, N., Sharma, V.: On second order duality of minimax fractional programming with square root term involving generalized B-(p,r)-invex functions. Ann. Oper. Res. 244, 603–617 (2016)
Acknowledgements
Indira P. Debnath is grateful to the Ministry of Human Resource and Development, India for financial support, to carry out this work.
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Debnath, I.P., Gupta, S.K. & Dangar, D. Remarks on duality for second order minimax fractional programming with B-(p,r)-invex functions. OPSEARCH 55, 196–201 (2018). https://doi.org/10.1007/s12597-017-0321-x
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DOI: https://doi.org/10.1007/s12597-017-0321-x
Keywords
- Minimax programming
- Fractional programming
- Nondifferentiable programming
- Second order duality
- B-(p,r)-invexity