Exploiting Band Structure 
             in Unconstrained Optimization Without Derivatives

                    B. Colson and Ph. L. Toint

This paper is concerned with derivative-free unconstrained optimization. We
first discuss a method combining the use of interpolation polynomials and
trust-region techniques to minimize a function whose derivatives are not
available.  We then show how the resulting algorithm may be adapted in a
suitable way to consider problems for which the Hessian matrix is known to be
banded. Numerical experiments confirm the favourable behaviour of the method
and in particular the advantages in terms of storage, function evaluations and
speed.