An Adaptive Nonlinear Least Square Algorithm

John E. Dennis, David M. Gay and Roy E. Welsch

No 196, NBER Working Papers from National Bureau of Economic Research, Inc

Abstract: NL2SOL is a modular program for solving the nonlinear least-squares problem that incorporates a number of novel features. It maintains a secant approximation S to the second-order part of the least-squares Hessian and adaptively decides when to use this approximation. We have found it very helpful to "size" S before updating it, something which looks much akin to Oren-Luenberger scaling. Rather than resorting to line searches or Levenberg-Marquardt modifications, we use the double-dogleg scheme of Dennis and Mei together with a special module for assessing the quality of the step thus computed. We discuss these and other ideas behind NLZSOL and briefly describe its evolution and current implementation.

Date: 1977-08
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Published as John E. Dennis & David M. Gay & Roy E. Walsh, 1981. "An Adaptive Nonlinear Least-Squares Algorithm," ACM Transactions on Mathematical Software, vol 7(3), pages 348-368.

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