A modular system of algorithms for unconstrained minimization

A new package, UNCMIN, for finding a local minimizer of a real valued function of more than one variable that is a modular system of algorithms, containing three different step selection strategies that may be combined with either analytic or finite difference gradient evaluation and witheither analytic, finite difference, or BFGS Hessian approximation.

Abstract

We describe a new package, UNCMIN, for finding a local minimizer of a real valued function of more than one variable. The novel feature of UNCMIN is that it is a modular system of algorithms, containing three different step selection strategies (line search, dogleg, and optimal step) that may be combined with either analytic or finite difference gradient evaluation and with either analytic, finite difference, or BFGS Hessian approximation. We present the results of a comparison of the three step selection strategies on the problems in More, Garbow, and Hillstrom in two separate cases: using finite difference gradients and Hessians, and using finite difference gradients with BFGS Hessian approximations. We also describe a second package, REVMIN, that uses optimization algorithms identical to UNCMIN but obtains values of user-supplied functions by reverse communication.