TOMS611 (See predecessor TOMS573 and successor TOMS717.)


Unconstrained minimization.


Gay, David M. (1983). ALGORITHM 611. Subroutines for unconstrained minimization using a model/trust region approach. ACM Transactions on Mathematical Software, 9(4), 503-524.

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.


This paper describes a set of subroutines designed to solve general unconstrained optimization problems for which it is feasible to work explicitly with either the Hessian of the objective function or an approximation to it. Subroutines SMSNO()and SUMSL() use a secant approximation to the Hessian. SMSNO() uses a slight variant of Stewart’s scheme to compute a finite difference approximation to the gradient, while SUMSL() obtains the gradient from a subroutine provided by the caller. Both of these routines compute steps by the double-dogleg technique of Dennis and Mei [1979]. Subroutine HUMSL() requires the caller to provide the gradient and Hessian of the objective function and it uses the Hessian to compute optimal locally constrained steps. All three subroutines use an explicit scale vector, and all three use the stopping tests of version 2.2 of NL2SOL() [Dennis, Gay, and Welsch, 1981, TOMS573]. These subroutines share many modules and offer the option of providing function and gradient, or function, gradient, and Hessian values by reverse communication. In this respect they exemplify what we believe is a good way to structure optimization software. [Gay, 1983, Introduction, p. 503.]


Fortran 77


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ORIGINAL CODE LOCATION (Fortran 77) (Fortran 90)