Nonlinear optimization is a mathematical approach used to find the best solutions for problems where the objective function or constraints exhibit nonlinear relationships. Unlike linear optimization, which deals with linear equations, nonlinear optimization accommodates more complex, curved relationships. It is crucial because many real-world problems involve nonlinearity, such as optimizing complex engineering designs, financial portfolios, or machine learning models. By addressing nonlinearity, nonlinear optimization helps businesses and researchers make more accurate and efficient decisions, leading to improved outcomes in various domains.