J. Comp. Math., 6 (1988), pp. 355-374.


A Memoryless Augmented Gauss-Newton Method For Nonlinear Least-Squares Problems

J. E. Dennis 1, Song-bai Sheng 2, Anh Vu Phuong 3

1 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
Abstract

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.

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