Extended Global Convergence Framework for Unconstrained

An extension of the global convergence framework for unconstrained derivative free optimization methods is presented. The extension makes it possible for the framework to include optimization methods with varying cardinality of the ordered direction set. Grid-based search methods are shown to be a special case of the more general extended global convergence framework. Furthermore, the required properties of the sequence of ordered direction sets listed in the definition of grid-based methods are relaxed and simplified by removing the requirement of structural equivalence.