Volume 27 , Issue 1 , PP: 159-175, 2026 | Cite this article as | XML | Html | PDF | Full Length Article
Maissam Jdid 1 * , Florentin Smarandache 2
Doi: https://doi.org/10.54216/IJNS.270116
A mathematical model consists of decision variables, a goal function, and constraints. The region of possible solutions for a nonlinear mathematical model is the set of vectors whose components satisfy all constraints. The optimal solution is the vector whose components satisfy all constraints, and at which the function reaches an optimal value (maximum or minimum). Nonlinear programming constitutes an important and fundamental part of operations research and is more comprehensive than linear programming. Its applications have spread across all branches of science, including engineering, physics, chemistry, management, economics, and military fields, among others. Nonlinear programming can also be used in forecasting, estimation, applied statistics, and determining the costs resulting from the production, purchase, and storage of goods. Given this importance, and in order to obtain a more accurate solution that takes into account all the changes that the system under study may be exposed to, we have previously presented a neutrosophic study of nonlinear models and some of the methods used to find the optimal solution. In addition to what we have previously done, in a research we present an improvement to the gradient projection method used to find the optimal solution for nonlinear models constrained by equal constraints, enabling us to obtain the optimal solution in fewer steps. We will then apply it to find the solution. Optimization of nonlinear neutrosophic models.
Nonlinear models , Neutrosophic logic , Neutrosophic nonlinear models constrained by equality constraints , Gradient projection method
[1] F. Smarandache and M. Jdid, “Research in the field of neutrosophic operations research volume (1),” 2021. [Online]. Available: https://fs.unm.edu/NeutrosophicOperationsResearch.pdf.
[2] M. M. Takallo, H. Bordbar, R. A. Borzooei, and Y. B. Jun, “BMBJ-neutrosophic ideals in BCK/BCI-algebras,” Neutrosophic Sets and Systems, vol. 27, pp. 1-16, 2019. [Online]. Available: https://fs.unm.edu/nss8/index.php/111/article/view/527.
[3] G. R. Rezaei, Y. B. Jun, and R. A. Borzooei, “Neutrosophic quadruple a-ideals,” Neutrosophic Sets and Systems, vol. 31, pp. 266-281, 2020. [Online]. Available: https://fs.unm.edu/nss8/index.php/111/article/view/447.
[4] B. Basumatary, N. Wary, and S. Broumi, “On some properties of interior, closure, boundary and exterior of neutrosophic multi topological space,” International Journal of Neutrosophic Science, vol. 17, no. 1, pp. 30-40, 2021. doi: 10.54216/IJNS.170102.
[5] E. Gonzalez-Caballero, “Applications of NeutroGeometry and AntiGeometry in real world,” International Journal of Neutrosophic Science, vol. 21, no. 1, pp. 14-32, 2023. doi: 10.54216/IJNS.210102.
[6] M. Jdid, F. Smarandache, and T. Fujita, “Neutrosophic augmented Lagrange multipliers method nonlinear programming problems constrained by inequalities,” Neutrosophic Sets and Systems, vol. 81, pp. 741-752, 2025. [Online]. Available: https://fs.unm.edu/nss8/index.php/111/article/view/5929.
[7] M. Jdid and F. Smarandache, “Unconstrained neutrosophic nonlinear programming problems gradient projection method,” International Journal of Neutrosophic Science, vol. 26, no. 3, pp. 279-286, 2025. doi: 10.54216/IJNS.260320.
[8] G. V. Reklaitis, A. Ravindran, and K. M. Ragsdell, Engineering Optimization: Methods and Applications, Wiley, Interscience, New York, 1983.
[9] J. S. Bakaja, W. Mualla, and others, Operations Research Book, translated into Arabic, The Arab Center for Arabization, Translation, Authoring and Publishing, Damascus, 1998.
[10] D. G. Luenberger and Y. Ye, Linear and Nonlinear Programming, Springer Science, Business Media, 2015.
[11] M. D. Al Hamid, Mathematical Programming, Aleppo University, Syria, 2010.
