Using Problem Structure in Derivative-free Optimization

                            Ph. L. Toint
                     Report 05/09  December 2005

Derivative-free unconstrained optimization is the class of optimization
methods for which the derivatives of the objective function are
unavailable. These methods are already well-studied, but are typically
restricted to problems involving a small number of variables.  The paper
discusses how this restriction may be removed by the use the underlying
problems structure, both in the case of pattern-search and interpolation
methods. The focus is on partially separable objective function, but it is
shown how Hessian sparsity, a weaker structure description, can also be
used to advantage.