Minmax fractional programming problem involving generalized convex functions

Anurag Jayswal; I.M. Stancu-Minasian; Dilip Kumar

doi:10.33993/jnaat411-968

Authors

Anurag Jayswal Indian School of Mines, India
I.M. Stancu-Minasian Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, Romania
Dilip Kumar Birla Institute of Technology, India

DOI:

https://doi.org/10.33993/jnaat411-968

Keywords:

minmax fractional programming, (\(F, \alpha, \rho, d\))-type I functions, second order duality

Abstract views: 259

Abstract

In the present study we focus our attention on a minmax fractional programming problem and its second order dual problem. Duality results are obtained for the considered dual problem under the assumptions of second order \(\left( {F,\alpha ,\rho ,d}\right) \) -type I functions.

Downloads

Download data is not yet available.

References

I. Ahmad and Z. Husain, Duality in nondifferentiable minimax fractional programming with generalized convexity, Appl. Math. Comp., 176, pp. 545-551, 2006. https://doi.org/10.1016/j.amc.2005.10.002 DOI: https://doi.org/10.1016/j.amc.2005.10.002

I. Ahmad, Z. Husain and S. Sharma, Second-order duality in nondifferentiable minmax programming involving type-I functions, J. Comp. Appl. Math., 215, pp. 91-102, 2008. https://doi.org/10.1016/j.cam.2007.03.022 DOI: https://doi.org/10.1016/j.cam.2007.03.022

C.R. Bector, S. Chandra and I. Husain, Second order duality for a minimax programming problem, Opsearch, 28, pp. 249-263, 1991.

S. Chandra and V. Kumar, Duality in fractional minimax programming, J. Austral. Math. Soc. Ser. A, 58, pp. 376-386, 1995. https://doi.org/10.1017/s1446788700038362 DOI: https://doi.org/10.1017/S1446788700038362

J.P. Crouzeix, J.A. Ferland and S. Schaible, Duality in generalized fractional programming, Math. Programming, 27, pp. 342-354, 1983. https://doi.org/10.1007/bf02591908 DOI: https://doi.org/10.1007/BF02591908

M. Hachimi and B. Aghezzaf, Second order duality in multiobjective programming involving generalized type-I functions, Numer. Funct. Anal. Optim., 25, pp. 725-736, 2004. https://doi.org/10.1081/nfa-200045804 DOI: https://doi.org/10.1081/NFA-200045804

M.A. Hanson, Second order invexity and duality in mathematical programming, Opsearch 30, pp. 313-320, 1993.

Z. Husain, I. Ahmad and S. Sharma, Second order duality for minmax fractional programming, Optim. Lett., 3, pp. 277-286, 2009. https://doi.org/10.1007/s11590-008-0107-4 DOI: https://doi.org/10.1007/s11590-008-0107-4

Z.A. Liang, H.X. Huang and P. Pardalos, P.M., Optimality conditions and duality for a class of nonlinear fractional programming problems, J. Optim. Theory Appl., 110, pp. 611-619, 2001. https://doi.org/10.1023/a:1017540412396 DOI: https://doi.org/10.1023/A:1017540412396

Z. Liang and Z. Shi, Optimality conditions and duality for a minimax fractional programming with generalized convexity, J. Math. Anal. Appl., 277, pp. 474-488, 2003. https://doi.org/10.1016/s0022-247x(02)00553-x DOI: https://doi.org/10.1016/S0022-247X(02)00553-X

J.C. Liu and C.S. Wu, On minimax fractional optimality conditions with (F,ρ)-convexity, J. Math. Anal. Appl, 219, pp. 36-51 1998. https://doi.org/10.1006/jmaa.1997.5785 DOI: https://doi.org/10.1006/jmaa.1997.5785

X.J. Long and J. Quan, Optimality conditions and duality for minimax fractional programming involving nonsmooth generalized univexity, Numer. Algebra Control Optim. 1, pp. 361-370, 2011. https://doi.org/10.3934/naco.2011.1.361 DOI: https://doi.org/10.3934/naco.2011.1.361

O.L. Mangasarian, Second and higher order duality in nonlinear programming, J. Math. Anal. Appl. 51, pp. 607-620, 1975. https://doi.org/10.1016/0022-247x(75)90111-0 DOI: https://doi.org/10.1016/0022-247X(75)90111-0

Q. Hu, G. Yang and J. Jian, On second order duality for minimax fractional programming, Nonlinear Anal. Real World Appl., 12, pp. 3509-3514, 2011. https://doi.org/10.1016/j.nonrwa.2011.06.011 DOI: https://doi.org/10.1016/j.nonrwa.2011.06.011

Q. Hu, Y. Chen and J. Jian, Second-order duality for nondifferentiable minimax fractional programming, Int. J. Comput. Math., 89, pp. 11-16, 2012. https://doi.org/10.1080/00207160.2011.631529 DOI: https://doi.org/10.1080/00207160.2011.631529

S.R. Yadav and R.N. Mukherjee, Duality for fractional minimax programming problems, J. Austral. Math. Soc. Ser. B, 31, pp. 482-492, 1990. https://doi.org/10.1017/s0334270000006809 DOI: https://doi.org/10.1017/S0334270000006809

X.M. Yang and S.H. Hou, On minimax fractional optimality and duality with generalized convexity, J. Global Optim., 31, pp. 235-252, 2005. https://doi.org/10.1007/s10898-004-5698-4 DOI: https://doi.org/10.1007/s10898-004-5698-4

J. Zhang and B. Mond, Second order duality for multiobjective nonlinear programming involving generalized convexity, in: B.M. Glover, B.D. Craven, D. Ralph (eds.), Proceeding of Optimization Miniconference III, University of Ballarat, pp. 79-95, 1997.