TOMS717 (See predecessors TOMS573 and TOMS611.)
Unconstrained or simply bounded minimization.
Bunch, David S., Gay, David M., and Welsch, Roy E. (1993). Algorithm 717. Subroutines for maximum likelihood and quasi-likelihood estimation of parameters in nonlinear regression models. ACM Transactions on Mathematical Software, 19(1), 109-130.
Gay, David M., and Welsch, Roy E. (1988). Maximum likelihood and quasi-likelihood for nonlinear exponential family regression models. Journal of the American Statistical Association, 83(404), 990-998.
ABSTRACT OR SUMMARY
We present Fortran 77 subroutines that solve statistical parameter estimation problems for general nonlinear models, e.g., nonlinear least-squares, maximum likelihood, maximum quasi-likelihood, generalized nonlinear least-squares, and some robust fitting problems. The accompanying test examples include members of the generalized linear model family, extensions using nonlinear predictors (“nonlinear GLIM”), and probabilistic choice models, such as linear-in-parameter multinomial probit models. The basic method, a generalization of the NL2SOL algorithm for nonlinear least-squares, employs a model/trust region scheme for computing trial steps, exploits special structure by maintaining a secant approximation to the second-order part of the Hessian, and adaptively switches between Gauss-Newton and an augmented Hessian approximation. Gauss-Newton steps are computed using a corrected seminormal equations approach. The subroutines include variants that handle simple bounds on the parameters, and that compute approximate regression diagnostics. [Bunch, Gay, Welsch, 1993, p. 109.]
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
Gay, David M. (October, 1990). Usage Summary for Selected Optimization Routines. [Computing Science Technical Report No. 153.] Murray Hill, NJ: AT&T Bell Laboratories. (Regarding PORT3 Library: http://cm.bell-labs.com/cm/cstr/153.ps.gz or http://citeseer.ist.psu.edu/gay90usage.html)
Gay, David M. (September, 1991). Driver PMAIN for DGL[FG][B]. (http://www.netlib.org/opt/nlr/usage.ps)