Report Number: CS-TR-89-1244
Institution: Stanford University, Department of Computer Science
Title: Software Performance on Nonlinear Least-Squares Problems
Author: Fraley, Christina
Date: January 1989
Abstract: This paper presents numerical results for a large and varied set of problems using sofware that is widely available and has undergone extensive testing. The algorithms implemented in this software include Newton-based linesearch and trust-region methods for unconstrained optimization, as well as Gauss-Newton, Levenberg-Marquardt, and special quasi-Newton methods for nonlinear least squares. Rather than give a critical assessment of the software itself, our original purpose was to use the best available software to compare the underlying algorithms, to identify classes of problems for each method on which the performance is either very good or very poor and to provide benchmarks for future work in nonlinear least squares and unconstrained optimization. The variability in the results made it impossible to meet either of the first two goals; however the results are significant as a step toward explaining why thesse aims are so difficult to accomplish.
http://i.stanford.edu/pub/cstr/reports/cs/tr/89/1244/CS-TR-89-1244.pdf