Higher order symmetric duality for multiobjective fractional programming problems over cones

Authors

  • Arshpreet Kaur School of Mathematics, Thapar Institute of Engineering and Technology (Deemed University), Patiala, India
  • Mahesh Kumar Sharma School of Mathematics, Thapar Institute of Engineering and Technology (Deemed University), Patiala, India

DOI:

https://doi.org/10.2298/YJOR200615012K

Keywords:

Higher order symmetric duality, Higher order (Ф,ρ)-convexity, Fractional Programs, Nondifferentiable programs, Generalized convexity

Abstract

This article studies a pair of higher order nondifferentiable symmetric fractional programming problem over cones. First, higher order cone convex function is introduced. Then using the properties of this function, duality results are set up, which give the legitimacy of the pair of primal dual symmetric model.

References

Bazaraa, M. S., and Goode, J. J., “On symmetric duality in nonlinear programming,” Operations Research, 21 (1) (1973) 1–9.

Bector, C. R., and Chandra, S., “Second order symmetric and self dual programs,” OPSEARCH, 23 (2) (1986) 89–95.

Caristi, G., Ferrara, M., and Stefanescu, A., “Mathematical programming with (φ, ρ) invexity,” in: Generalized Convexity and Related Topics, Springer, 167–176, 2007.

Chandra, S., Craven, B. D., and Mond, B., “Symmetric dual fractional programming,” Mathematical Methods of Operations Research, 29 (1985) 59–64.

Chen, X., “Higher-order symmetric duality in nondifferentiable multiobjective programming problems,” Journal of Mathematical Analysis and Applications, 290 (2) (2004) 423–435.

Dantzig, G., Eisenberg, E., and Cottle, R., “Symmetric dual nonlinear programs,” Pacific Journal of Mathematics, 15 (3) (1965) 809–812.

Dorn, W., “A symmetric dual theorem for quadratic programs,” Journal of Operations Research Society of Japan, 2 (3) (1960) 93–97.

Dubey, R., and Gupta, S. K., “Duality for a nondifferentiable multiobjective higher-order symmetric fractional programming problems with cone constraints,” Journal of Nonlinear Analysis and Optimization: Theory & Applications, 7 (2016) 1–15.

Gulati, T. R., and Gupta, S. K., “Higher-order symmetric duality with cone constraints,” Applied Mathematics Letters, 22 (5) (2009) 776–781.

Gulati, T. R., Husain, I., and Ahmed, A., “Multiobjective symmetric duality with invexity,” Bulletin of the Australian Mathematical Society, 56 (1) (1997) 25–36.

Gulati, T. R., and Mehndiratta, G., “Nondifferentiable multiobjective Mond–Weir type second-order symmetric duality over cones,” Optimization Letters, 4 (2010) 293–309.

Gupta, S. K., Kailey, N., and Sharma, M. K., “Higher-order (F, α, ρ, d)-convexity and symmetric duality in multiobjective programming,” Computers & Mathematics with Applications, 60 (8) (2010) 2373–2381.

Jayswal, A., and Jha, S., “Second order symmetric duality in fractional variational problems over cone constraints,” Yugoslav Journal of Operations Research, 28 (1) (2018) 39–57.

Kapoor, M., “Vector optimization over cones involving support functions using generalized (φ, ρ)-convexity,” OPSEARCH, 54 (2) (2017) 351–364.

Kharbanda, P., and Agarwal, D., “Non-smooth multi-objective fractional programming problem involving higher order functions,” International Journal of Computing Science and Mathematics, 10 (4) (2019) 351–363.

Kim, M. H., and Kim, D. S., “Non-differentiable symmetric duality for multiobjective programming with cone constraints,” European Journal of Operational Research, 188 (3) (2008) 652–661.

Kim, D. S., Yun, Y. B., and Lee, W. J., “Multiobjective symmetric duality with cone constraints,” European Journal of Operational Research, 107 (3) (1998) 686–691.

Mishra, S. K., “Multiobjective second order symmetric duality with cone constraints,” European Journal of Operational Research, 126 (3) (2000) 675–682.

Mond, B., and Schechter, M., “Non-differentiable symmetric duality,” Bulletin of the Australian Mathematical Society, 53 (2) (1996) 177–188.

Singh, V., Jayswal, A., Al-Homidan, S., and Ahmad, I., “Higher order duality for cone vector optimization problems,” Asian-European Journal of Mathematics, 13 (1) (2020) 2050020 1–15.

Suneja, S. K., and Louhan, P., “Higher-order symmetric duality under cone-invexity and other related concepts,” Journal of Computational and Applied Mathematics, 255 (C) (2014) 825–836.

Tripathy, A. K., and Devi, G., “Wolfe type higher order multiple objective nondifferentiable symmetric dual programming with generalized invex function,” Journal of Mathematical Modelling and Algorithms in Operations Research, 13 (2014) 557–577.

Verma, K., Verma, J. P., and Ahmad, I., “A new approach on multiobjective higher-order symmetric duality under cone-invexity,” Bulletin of the Malaysian Mathematical Sciences Society, 44 (2020) 479–495.

Weir, T., “Symmetric dual multiobjective fractional programming,” Journal of the Australian Mathematical Society, 50 (1) (1991) 67–74.

Yang, X.-M., and Hou, S.-H., “Second-order symmetric duality in multiobjective programming,” Applied Mathematics Letters, 14 (5) (2001) 587–592.

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Published

2022-02-01

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Section

Research Articles