Computational Intelligence and Mathematical Applications

Mathematical optimization plays a fundamental role in engineering, economics, healthcare, logistics, and artificial intelligence systems. Traditional optimization methods, including linear programming, gradient-based algorithms, and heuristic approaches, often struggle when dealing with high-dimensional, non-convex, and large-scale problems. The increasing complexity of real-world optimization challenges necessitates intelligent and adaptive computational techniques. This paper addresses the problem of solving complex mathematical optimization tasks using deep learning-based neural network models. The proposed approach investigates how deep neural networks (DNNs) can approximate optimal solutions for constrained and unconstrained optimization problems. Instead of relying solely on classical iterative solvers, neural networks are trained to learn mappings between problem parameters and near-optimal solutions. Supervised learning and reinforcement learning paradigms are analyzed for optimization tasks. The study integrates feed forward neural networks and deep architectures with gradient-based training mechanisms to enhance convergence and solution quality. Experimental analysis demonstrates that neural network-based optimization models significantly reduce computational time while maintaining competitive accuracy compared to traditional optimization techniques. The results indicate improved scalability for high- dimensional problems and robustness in handling non-linear objective functions. The impact of this research lies in establishing deep learning as a viable mathematical optimization framework capable of transforming computational intelligence applications. The findings suggest that neural networks can serve not only as predictive tools but also as efficient optimization solvers for next-generation intelligent systems.