Abstract
AbstractIn this article, we present generalizations of the cone-preinvexity functions and study a pair of second-order symmetric solutions for multiple objective nonlinear programming problems under these generalizations of the cone-preinvexity functions. In addition, we establish and prove the theorems of weak duality, strong duality, strict converse duality, and self-duality by assuming the skew-symmetric functions under these generalizations of the cone-preinvexity functions. Finally, we provide four nontrivial numerical examples to demonstrate that the results of the weak and strong duality theorems are true.
Publisher
Springer Science and Business Media LLC
Subject
Computational Theory and Mathematics,General Engineering,Theoretical Computer Science,Software,Applied Mathematics,Computational Mathematics,Numerical Analysis
Reference22 articles.
1. Devi, G.: Symmetric duality for nonlinear programming involving bonvex functions. Eur. J. Oper. Res. 104, 615–621 (1998)
2. Duber, R., Vandana., Mishra, V.N..: Second-order multiple objective symmetric programming problem and duality relations under -convexity. Glob. J. Eng. Sci. Res. 5(8), 187−199 (2018)
3. Dubey, R., Vandana., Mishra, V.N., Karateke, S.: A class of second order non-differentiable symmetric duality relations under generalized assumptions. J. Math. Comput. Sci. 21(2), 120–126 (2020). https://doi.org/10.2243/jmcs.021.02.03.
4. Dubey, R., Mishra, L.N., Ruiz, L.M.: Non-differentiable Mond-Weir type multiple objective symmetric fractional problem and their duality theorems under generalized assumptions. Symmetric 11(11), 1348–1365 (2019). https://doi.org/10.3390/sym11111348
5. Dubey, R., Mishra, L.N.: Non-differentiable multiple objective higher-order duality relations for unified type dual models under type-I functions. Adv. Stud. Cotemp. Math. (Kyung Shang) 29(3), 373–382 (2019). https://doi.org/10.17777/ascm2019.29.3.373