Duality for a class of second order symmetric nondifferentiable fractional variational problems

Authors

  • Ashish Kumar Prasad Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, India
  • Anant Pratap Singh Department of Mathematical Sciences, Indian Institute of Technology(BHU), Varanasi, India
  • Sony Khatri Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, India

DOI:

https://doi.org/10.2298/YJOR190215004P

Keywords:

Symmetric Duality, Variational Problem, Second Order F-convexity, Non-differentiable Programming.

Abstract

The present work frames a pair of symmetric dual problems for second order nondifferentiable fractional variational problems over cone constraints with the help of support functions. Weak, strong and converse duality theorems are derived under second order F-convexity assumptions. By removing time dependency, static case of the problem is obtained. Suitable numerical example is constructed.

References

Ahmad, I., Sharma, S. "Symmetric duality for multiobjective fractional variational problems involving cones", European Journal of Operational Research, 188 (3) (2008) 695-704.

Ahmad, I., Yaqub, M., Ahmed, A. "Symmetric duality for fractional variational problems with cone constraints", Journal of Applied Mathematics and Computing, 23 (1) (2007) 281-292.

Ahmad, I., Gulati, T.R. "Mixed type duality for multiobjective variational problems with generalized (F)-convexity", Journal of Mathematical Analysis and Applications, 306 (2) (2005) 669-683.

Bector, C.R., Chandra, S. "Second order symmetric and self dual programs", Opsearch, 23 (1986) 89-95.

Dorn, W.S. "A symmetric dual theorem for quadratic programs", Journal of the Operations Research Society of Japan, 2 (1960) 93-97.

Hou, S.H., Yang, X.M. "On second-order symmetric duality in nondifferentiable programming", Journal of Mathematical Analysis and Applications, 255 (2) (2001) 491-498.

Husain, I., Ahmed, A., Masoodi, M. "Second-order duality for variational problems", European Journal of Pure and Applied Mathematics, 2 (2) (2009) 278-295.

Jayswal, A., Jha, S., Prasad, A.K., Ahmad, I. "Second-order symmetric duality in variational control problems over cone constraints", Asia-Pacific Journal of Operational Research, 35 (4) (2018).

Jayswal, A., Jha, S. "Second order symmetric duality in fractional variational problems over cone constraints", Yugoslav Journal of Operational Research, 28 (1) (2018) 39-57.

Jayswal, A., Prasad, A.K. "Second order symmetric duality in nondifferentiable multiobjective fractional programming with cone convex functions", Journal of Applied Mathematics and Computing, 45 (1) (2014) 15-33.

Kailey, N., Gupta, S.K. "Duality for a class of symmetric nondifferentiable multiobjective fractional variational problems with generalized (F^d)-convexity", Mathematical and Computer Modelling, 57 (2013) 1453-1465.

Mangasarian, O.L. "Second order and higher order duality in nonlinear programming", Journal of Mathematical Analysis and Applications, 51 (1975) 607-620.

Mond, B., Schechter, M. "Non-differentiable symmetric duality", Bulletin of the Australian Mathematical Society, 53 (1996) 177-188.

Mond, B., Chandra, S., Husain, I. "Duality for variational problems with invexity", Journal of Mathematical Analysis and Applications, 134 (1988) 322-328.

Nahak, C., Nanda, S. "On efficiency and duality for multiobjective variational control problems with (F, ε)-convexity", Journal of Mathematical Analysis and Applications, 209 (1997) 415-434.

Saini, H., Gulati, T.R. "Nondifferentiable multiobjective symmetric duality with F-convexity over cones", Nonlinear Analysis: Theory, Methods & Applications, 74 (5) (2011) 1577-1584.

Yang, X.M., Yang, X.Q., Teo, K.L. "Nondifferentiable second order symmetric duality in mathematical programming with F-convexity", European Journal of Operational Research, 144 (3) (2003) 554-559.

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Published

2020-05-01

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Section

Research Articles