**NAME**

TOMS573 or NL2SOL (See successors TOMS611 and TOMS717.)

**PURPOSE**

Solving nonlinear least-squares problems (unconstrained optimization).

**REFERENCE**

Dennis, John E., Jr., Gay, David M., and Welsch, Roy E. (1981b). ALGORITHM 573. NL2SOL – An adaptive nonlinear least-squares algorithm. *ACM Transactions on Mathematical Software*, **7**(3), 369-383.

Dennis, John E., Jr., Gay, David M., and Welsch, Roy E. (1981a). An adaptive nonlinear least-squares algorithm. *ACM Transactions on Mathematical Software*, **7**(3), 348-368.

**ABSTRACT OR SUMMARY**

Given a continuously differentiable function (residual vector) *R(x) = (R*_{1}(x), R_{2}(x),...,R_{n}(x))^{T} of p parameters *x = (x*_{1}, x_{2},..., x_{p})^{T}, NL2SOL attempts to find a parameter vector *x** that minimizes the sum-of-squares function F(x) = Sum R_{i}^{2}. [Dennis, Gay, and Welsch, 1981b, p. 369.]

NL2SOL is a modular program for solving nonlinear least-squares problems 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. S is “sized” before updating, something that is similar to Oren-Luenberger scaling. The step choice algorithm is based on minimizing a local quadratic model of the sum of squares function constrained to an elliptical trust region centered at the current approximate minimizer. This is accomplished using ideas discussed by Moré, together with a special module for assessing the quality of the step thus computed. These and other ideas behind NL2SOL are discussed, and its evolution and current implementation are also described briefly. [Dennis, Gay, and Welsch, 1981a, p. 348.]

**LANGUAGE**

Fortran 77.

**LICENSE**

All software, both binary and source published by the Association for Computing Machinery (hereafter, Software) is copyrighted by the Association (hereafter, ACM) and ownership of all right, title and interest in and to the Software remains with ACM. By using or copying the Software, User agrees to abide by the terms of this Agreement. The URL for the ACM Software Copyright and License Agreement is __http://www.acm.org/pubs/copyright_policy/softwareCRnotice.html__.

**ORIGINAL CODE LOCATION**

__http://www.netlib.org/toms/573__

**TECHNICAL NOTES**

None.

**DOWNLOAD**

None.