Using Problem Structure in Derivative-free Optimization

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.