aspg-34-3872-1792226099 20261017083459 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Prospects for Applied Mathematics and Data Analysis PAMDA 2836-4449 2024 4 2 Maissam Jdid Faculty of Science, Damascus University, Damascus, Syria; Department of Requirements, International University for Science and Technology, Ghabageb, Syrian Arab Republic Mathematical examples rely on constructing mathematical models consisting of an objective function and constraints. These models may be linear, nonlinear, or otherwise. The objective function is either a maximization function or a minimization function for a given quantity. Nonlinear programming constitutes an important and fundamental part of operations research and is more comprehensive than linear programming. Therefore, researchers have focused on presenting studies that help find the optimal solution to these problems. Most of these studies have focused on the importance of knowing the type of objective function—whether it is convex or concave—because this knowledge helps determine the type of maximum value we obtain when studying a nonlinear programming problem. The Hessian matrix was used for this purpose. In this research, we will present the most important concepts that can be used when determining the type of maximum value for a nonlinear programming problem, as mentioned in some classic references. We will then reformulate them using the concepts of neutrosophic logic. 2024 09 14 3872 https://creativecommons.org/licenses/by/4.0/ 10.54216/PAMDA.040202 https://americaspg.com/journal/34/article/3872 https://americaspg.com/storage/articles/manuscripts/01M1MVM6T03A1C6BA21G4AT24E.pdf