Nonlinear constrained optimization is really at the heart of computational mathematics, ranging from resource allocation to material stress analysis. The contribution of this paper is a sophisticated optimization framework that harnesses trust-region methods, dynamic regularization, and thorough sensitivity analysis to solve high-dimensional nonlinear problems. The proposed method minimizes an objective function comprising quadratic terms, linear penalties, and sparsityinducing regularization, subject to stress and budget constraints. The framework achieved precise convergence in 46 iterations and 756 function evaluations, satisfying the gtol termination condition with optimality of 4.43 × 10−9 and zero constraint violations, all within 0.36 seconds. To provide insight into the optimization process, the following four visualizations are generated: a Convergence Plot showing exponential convergence of the objective function that converges and stabilizes after approximately 100 iterations; a Gradient Magnitude Plot showing exponential decay in the gradient norm, confirming smooth and efficient convergence; a Hessian Matrix Heatmap showing the structure of the dependencies and curvature around the optimal solution to assist in sensitivity interpretation; and a Variable Contribution Bar Plot, which quantifies the relative contribution from each decision variable to the objective function to identify the dominant contributors. This work showcases the robustness, efficiency, and scalability of the proposed framework. The visualizations not only validate the results of the optimization but further give insight into the solution space. These results open up perspectives toward the extension of such a framework to more complex dynamic constraints and challenging real-world datasets, bringing important contributions to computational mathematics and applied optimization.