This paper describes UNCMIN, a modular system of FORTRAN subroutines for solving where x is an n-dimensional vector and f is a scalar function of x. The first and second derivatives of f should be continuous. This is an important restriction. Many real problems have discontinuous function values as well as first and second derivatives.
A nice feature of the package is its modular approach. It offers the following options:
(1) Three different step selection methods--line search, dogleg, and hookstep.
(2) Analytic or finite difference gradient evaluation.
(3) Analytic, finite difference, or BFGS Hessian calculation.
The Newton minimization algorithm is used to find the minimum. A large number of standard test functions were minimized using various choices from the above options. Some conclusions are: the choice of step selection method does not change the results much; and the BFGS Hessian approximation gives a smaller number of function evaluations compared to the finite difference Hessian. The ideas in this paper are explained in more detail in [1]. The reader who is interested in this approach to unconstrained minimization should read this book.
