A Memoryless Augmented Gauss-Newton Method For Nonlinear Least-Squares Problems
J. E. Dennis 1, Song-bai Sheng 2, Anh Vu Phuong 31 Mathematical Sciences Department, Rice University, Houston, Texas, USA 77251
2 Nanjing, University, Nanjing, China
3 International Mathematical and Statistical Libraries, 7500 Bellaire Blud, Houston, Texas, USA
Received 1987-4-1 Revised Online 2006-12-7
In this paper, we develop, analyze, and test a new algorithm for nonlinear least-squares problems. The algorithm uses a BFGS update of the Gauss-Newton Hessian when some heuristics indicate that the Gauss-Newton method may not make a good step. Some important elements are that the secant or quasi-Newton equations considered are not the obvious ones, and the method does not build up a Hessian approximation over several steps. The algorithm can be implemented easily as a modification of any Gauss-Newton code, and it seems to be useful for large residual problems.