Cooperative coevolutionary algorithms have the potential to significantly speed up the search process by dividing the space into parts that can each be conquered separately. However, recent research presented theoretical and empirical arguments that these algorithms tend to converge to suboptimal solutions in the search space, and are thus not fit for optimization tasks. This paper details an extended formal model for cooperative coevolutionary algorithms, and uses it to explore possible reasons these algorithms converge to optimal or suboptimal solutions. We demonstrate that, under specific conditions, this theoretical model will converge to the globally optimal solution. The proofs provide the underlying theoretical foundation for a better application of cooperative coevolutionary algorithms. We demonstrate the practical advantages of applying ideas from this theoretical work to a simple problem domain.