Advancing Mathematical Optimization Methods: Applications, Challenges, and Future Directions
Yiyang Zou · Theoretical and Natural Science · 2025
Mathematical optimization methods have seen substantial advancements and applications in diverse fields, including industry, agriculture, commerce, and scientific research, due to advances in computer science and artificial intelligence. These methods improve production efficiency, resource allocation, and structural optimization. This paper reviews key optimization techniques such as gradient descent, Newton’s method, and heuristic algorithms, discussing their advantages, limitations, and applicability. Although optimization methods offer powerful tools for solving complex equations and optimizing solutions, real-world scenarios often introduce challenges such as computational errors and model idealizations. The future of mathematical optimization lies in improving algorithm speed, usability, and accuracy, allowing broader accessibility and aligning solutions with practical realities. This exploration highlights both the current utility and the evolving potential of optimization techniques in addressing global challenges