Abstract
In the present article, we study naturally K-pseudoconvex and strongly K-pseudoconvex definition and also give existing numerical examples of functions of this kind, and under cones functions, we develop a novel type of non-differentiable multiobjective fractional symmetric dual programming of the Mond–Weir type and prove duality relations involving strongly K-pseudoinvexity assumptions. Our results generalize a number of previous findings in the literature.
Ramu Dubey and Lakshmi Narayan Mishra contributed equally to this work.
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References
Antczak, T. (2015). Saddle point criteria and Wolfe duality in nonsmooth \((\phi, \rho )\)-invex vector optimization problems with inequality and equality constraints. International Journal of Computer Mathematics, 92, 882–907.
Cambini, R. (1996). Some new classes of generalized concave vector-valued functions. Optimization, 36, 11–24.
Chinchuluun, A., Migdalas, A., Pardalos, P. M., & Pitsoulis, L. (2008). Pareto optimality, game theory and equilibria. Springer.
Dubey, R. (2019). Duality results for a class of mixed type dual models under type-I functions. Nonlinear Studies, 26, 1–14.
Dubey, R., & Mishra, V. N. (2019). Symmetric duality results for second-order nondifferentiable multiobjective programming problem. RAIRO Operations Research, 53, 539–558.
Dubey, R., & Mishra, V. N. (2020). Second-order nondifferentiable multiobjective mixed type fractional programming problems. International Journal of Nonlinear Analysis and Applications, 10, 1–213.
Dubey, R., Deepmala, & Mishra, V. N. (2020). Higher-order symmetric duality in nondifferentiable multiobjective fractional programming problem over cone constraints. Statistics Optimization and Information Computing,8, 187–205.
Egudo, R. R. (1988). Multiobjective fractional duality. Bulletin of the Australian Mathematical Society, 37, 367–378.
Jayswal, A., & Jha, S. (2018). Second order symmetric duality in fractional variational problems over cone constraints. Yugoslav Journal of Operations Research, 28, 39–57.
Kar, M. B., Kar, S., Guo, S., Li, X., & Majumder, S. (2019). A new bi-objective fuzzy portfolio selection model and its solution through evolutionary algorithms. Soft Computing,23, 4367–4381.
Kaur, A., & Sharma, M. K. (2021). Higher order symmetric duality for multiobjective fractional programming problems over cones. Yugoslav Journal of Operations Research. https://doi.org/10.2298/YJOR200615012K
Kharbanda, P., & Agarwal, D. (2019). Non-smooth multi-objective fractional programming problem involving higher order functions. International Journal of Computing Science and Mathematics, 10, 351.
Khurana, S. (2005). Symmetric duality in multiobjective programming involving generalized cone-invex functions. European Journal of Operational Research, 165, 592–597.
Majumder, S., Kar, S., & Pal, T. (2019). Uncertain multi-objective Chinese postman problem. Soft Computing, 23, 11557–11572.
Mishra, S. K., Samei, M. E., Chakraborty, S. K., & Ram, B. (2021). On \( q \)-variant of Dai-Yuan conjugate gradient algorithm for unconstrained optimization problems. Nonlinear Dynamics, 104, 2471–2496.
Oveisiha, M., & Zafarani, J. (2012). Vector optimization problem and generalized convexity. Journal of Global Optimization, 52, 29–43.
Suneja, S. K., Sharma, S., & Vani. (2008). Second-order duality in vector optimization over cones. Journal of Applied Mathematics & Informatics,26, 251–261.
Weir, T., Mond, B., & Craven, B. D. (1987). Weak minimization and duality. Numerical Functional Analysis and Optimization, 9, 181–192.
Acknowledgements
The first author acknowledges the J.C. Bose University of Science and Technology, YMCA, Faridabad, as well as the UGC, New Delhi, for giving funding financial support.
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Balram, Dubey, R., Mishra, L.N. (2023). Symmetric Duality for a Multiobjective Fractional Programming with Cone Objectives as Well as Constraints. In: Gunasekaran, A., Sharma, J.K., Kar, S. (eds) Applications of Operational Research in Business and Industries. Lecture Notes in Operations Research. Springer, Singapore. https://doi.org/10.1007/978-981-19-8012-1_22
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DOI: https://doi.org/10.1007/978-981-19-8012-1_22
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