A note on comparison of nonlinear least squares algorithms

The nonlinear least squares problem is a special case of the unconstrained minimization problem. While a large number of new algorithms have been developed in recent years, both for general unconstrained minimization and the least squares case, comparative studies are limited. Further, there has been practically a revolution in algorithm testing and comparison methodology. Recent advances include a more comprehensive performance criteria, use of large numbers of randomly generated test problems, and application of sophisticated statistical techniques for experiment design and data evaluation.These developments have made questionable the findings of the few earlier comparative studies of least squares algorithms. This creates a necessity of a comparative study employing current methodology that evaluates the specialized least squares algorithms along with a few general algorithms for unconstrained minimization.