Nonlinear least squares problems

Nonlinear least squares problems involve finding the best way to fit a mathematical model to data when the relationship between variables isn't a straight line. The goal is to adjust model parameters so that the difference between the model's predictions and the actual data is minimized, measured by the total of squared differences. Unlike simpler linear cases, nonlinear problems are more complex because the relationship is curved or more complicated. Advanced algorithms are used to iteratively tweak the parameters, seeking the best fit. These problems are common in fields like physics, biology, and engineering for modeling real-world phenomena.