A class of new type unified non-differentiable higher order symmetric duality theorems over arbitrary cones under generalized assumptions

Authors

  • Ramu Dubey Department of Mathematics, J.C. Bose University of Science and Technology, YMCA, Faridabad, India
  • Rajnish Kumar Department of Mathematics, School of Basic Sciences and Research, Sharda University, India
  • Khursheed Alam Department of Mathematics, School of Basic Sciences and Research, Sharda University, India
  • Mishra Lakshmi Narayan Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology (VIT) University, Vellore, Tamil Nadu, India
  • Mishra Vishnu Narayan Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur, Madhya Pradesh, India

DOI:

https://doi.org/10.2298/YJOR210218020D

Keywords:

Symmetric duality, Non-differentiable programming, Mixed duality, Arbitrary cones

Abstract

In the present paper, a newly combined higher-order non-differentiable symmetric duality in scalar-objective programming over arbitrary cones is formulated. In literature we have discussed primal-dual results with arbitrary cones, while in this article, we have derived combined result with one model over arbitrary cones. The theorems of duality are derived for these problems under η-pseudoinvexity/η-invexity/C-pseudoconvexity/C-convexity speculations over arbitrary cones.

References

Chen, X., "Higher-order symmetric duality in nondi erentiable multi-objective programming problems", Journal of Mathematical Analysis and Applications, 290 (2) (2004) 423- 435.

Chen, X. H., "Higher-order symmetric duality in nonlinear non-differentiable programs", Journal of Mathematical Analysis and Applications, 290 (2) (2004) 423-435.

Chandra, S., Husain, I., and Abha, "On mixed symmetric duality in mathematical programming", Opsearch, 36 (2) (1999) 165-171.

Dubey, R., Kumar, A., Ali, R., and Mishra, L. N., "New class of G-Wolfe-type symmetric duality model and duality relations under Gf -bonvexity over arbitrary cones", Journal of Inequalities and Applications, 30 (1) (2020) 1-16.

Dubey, R., Vandana, Mishra, V. N., and Karateke, S., "A class of second order nondifferentiable symmetric duality relations under generalized assumptions", Journal of Mathematics and Computer Science, 21 (2) (2020) 120-126.

Dubey, R., and Mishra, L. N., "Nondifferentiable multiobjective higher-order duality relations for unified type dual models under type-I functions", Advanced Studies in Contemporary Mathematics, 29 (2019) 373-382.

Dubey, R., and Mishra, V. N., "Nondifferentiable higher-order duality theorems for new type of new of dual model under generalized functions", Proyecciones Journal of Mathematics, 39 (2020) 15-29.

Dubey, R., Mishra, L. N., and Ali, R., "Special Class of Second-Order Non-Differentiable Symmetric Duality Problems with (G,αf)-Pseudobonvexity assumptions", Mathematics, 7 (8) (2019) 763.

Dubey, R., and Mishra, V. N., "Symmetric duality results for a nondi erentiable multiobjective programming problem with support function under strongly assumptions", RAIRO- Operations Research, 53 (2) (2019) 539-558.

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

Dantzig, G. B., "Symmetric dual nonlinear programs", Pacific Journal of Mathematics, 15 (1965) 809-812.

Gulati, T. R., and Verma, K., "Non-di erentiable higher order symmetric duality under generalized invexity", FILOMAT, 28 (8) (2014) 1661-1674.

Hou, S. H., and Yang, X. M., "On second-order symmetric duality in non-differentiable programming", Journal of Mathematical Analysis and Applications, 255 (2001) 488-491.

Kassem, M., and Abd, El-H., "Multiobjective nonlinear second order symmetric duality with (K,F)- pseudoconvexity", Applied Mathematics and Computation, 219 (2012) 2142- 2148.

Khurana, S., "Symmetric duality in multiobjective programming involving generalized cone-invex functions", European Journal of Operational Research, 165 (3) (2005) 592-597.

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

Mond, B., and Zhang, J., Higher-order invexity and duality in mathematical programming", in: J. P. Crouzeix, et al. (eds.), Generalized Convexity, Generalized Monotonicity: Recent Results, Kluwer Academic Dordrecht, (1998) 357-372.

Verma, K., and Gulati, T. R., "Wolfe type higher order symmetric duality under invexity", Journal of Applied Mathematics and Informatics, 32 (1-2) (2014) 153-159.

Verma, K., Mathur, P., and Gulati, T.R., "A new approach on mixed type nondi erentiable higher-order symmetric duality", Journal of the Operations Research Society of China, 7 (2) (2019) 321-335.

Xianjun, L., "Sufficiency and duality for nonsmooth multiobjective programming problems involving generalized univex functions", Journal of Systems Science and Complexity, 26 (6) (2013) 1002-1018.

Yang, X. M., Teo, K. L., and Yang, X. Q., "Mixed symmetric duality in non-differentiable mathematical programming", Indian Journal of Pure and Applied Mathematics, 34 (5) (2003) 805-815.

Downloads

Published

2022-05-01

Issue

Vol. 32 No. 2 (2022)

Section

Research Articles

License

Copyright (c) YUJOR

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.