A STUDY ON OPTIMIZATION METHODS IN NONLINEAR MATHEMATICAL MODELS

Abstract

This paper explores modern optimization methods applied to nonlinear mathematical models, which are widely used in engineering, economics, and data science. The study focuses on analyzing gradient-based and heuristic optimization techniques, including their efficiency, convergence properties, and applicability to complex systems. Special attention is given to constrained and unconstrained optimization problems, where objective functions exhibit nonlinearity and multiple local extrema. The research highlights the role of algorithms such as Gradient Descent, Newton’s Method, and Genetic Algorithms in solving real-world problems. Comparative analysis demonstrates the strengths and limitations of each approach, emphasizing the importance of selecting appropriate methods based on problem structure. The findings contribute to improving computational efficiency and accuracy in solving nonlinear optimization tasks