Abstract
We propose the idea of \((C,G_{f},\alpha ,\rho ,d)\)-invex function and give a significant numerical example which explains the existence of this type of functions. Moreover, we have established several generalized concepts, namely, \((F, G_{f}, \alpha , \rho , d)/(C, G_{f}, \alpha , \rho , d)\)-invexity and formulate a numerical example which satisfies feasible conditions of the given system. We consider Mond-Weir type fractional symmetric dual model over arbitrary cones and discuss duality theorems under \((C,G_{f},\alpha ,\rho ,d)\)-invexity assumptions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Verma, K., Mathur, P., Gulati, T.R.: A new approach on mixed type nondifferentiable higher order symmetric duality. J. Oper. Res. Soc. China (2018). https://doi.org/10.1007/s40305-018-0213-7
Gao, Y.: Higher order symmetric duality in multi-objective programming problems. Acta Mathematicae Applicate Sincia. English Series 32, 485–494 (2016)
Mishra, S.K.: Second order symmetric duality in mathematical programming with Fconvexity. Eur. J. Oper. Res. 127, 507–518 (2000)
Mond, B., Weir, T.: Generalized convexity and duality. In: Schaible, S., Ziemba, W.T. (eds.) Generalized Convexity in Optimization and Economics, pp. 263–280. Academic Press, New York (1981)
Hanson, M.A.: On sufficiency on the Kuhn-Tucker conditions. J. Math. Anal. Appl. 80, 545–550 (1981)
Antczak, T.: New optimality conditions and duality results of G-type in differentiable mathematical programming. Nonlinear Anal. 66, 1617–1632 (2007)
Antczak, T.: On G-invex multi-objective programming. Part I. Optimality. J. Global Optim. 43, 97–109 (2009)
Kang, Y.M., Kim, D.S., Kim, M.H.: Optimality conditions of G-type in locally Lipchitz multi-objective programming. Vietnam J. Math. 40, 275–285 (2012)
Ferrara, M., Viorica-Stefaneseu, M.: Optimality conditions and duality in multi-objective programming with \((\phi,\rho )\)-invexity. Yugoslav J. Oper. Res. 18, 153–165 (2008)
Viorica-Stefaneseu, M., Ferrara, M.: Multi-objective programming with new invexities. Optim. Lett. 7, 855–870 (2013)
Egudo, R.: Multi-objective fractional duality. Bull. Aust. Math. Soc. 37, 367–378 (1988)
Long, X.J.: Optimality conditions and duality for nondifferentiable multi-objective fractional programming problems with \((C,\alpha,\rho, d)\)-convexity. J. Optim. Appl. 148, 197–208 (2011)
Brumelle, S.: Duality for multiple objective convex programs. Math. Oper. Res. 6, 159–172 (1981)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Dubey, R., Singh, T., Vimal, V., Nautiyal, B. (2021). Multi-objective Symmetric Fractional Programming Problem and Duality Relations Under \((C,G_{f},\alpha ,\rho ,d)\)-Invexity over Cone Constraints. In: Abraham, A., Jabbar, M., Tiwari, S., Jesus, I. (eds) Proceedings of the 11th International Conference on Soft Computing and Pattern Recognition (SoCPaR 2019). SoCPaR 2019. Advances in Intelligent Systems and Computing, vol 1182. Springer, Cham. https://doi.org/10.1007/978-3-030-49345-5_26
Download citation
DOI: https://doi.org/10.1007/978-3-030-49345-5_26
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-49344-8
Online ISBN: 978-3-030-49345-5
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)