B.rmen, Árpád et al., Extended Global Convergence Framework for Unconstrained Optimization, Acta mathematica Sinica. English series (Print) , 20(3), 2004, pp. 433-440
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.