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.


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.]


Fortran 77


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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: or

Gay, David M. (September, 1991). Driver PMAIN for DGL[FG][B]. (