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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 S M S N O ( ) and S U M S L ( ) 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 [3]. 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( ) [2]. 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.

Algorithm 611: Subroutines for Unconstrained Minimization Using a Model/Trust-Region Approach