In a production environment that is more and more digitized, integrated, and connected, the coordination of complex physically coupled systems of systems is essential to ensure a resource efficient and optimal operation. Large petrochemical production sites or industrial clusters are such systems, where the coordination is challenging. The challenges are manifold. They result from a complex interplay of humans, algorithms, and technology. This thesis sketches a landscape of challenges for the coordination of coupled production systems and presents the foundations of the employed algorithms to coordinate these systems. Some of the barriers can be tackled by distributed market-like coordination algorithms that establish a micro market among the individual subsystems, where a certain level of confidentiality is realized, while at the same time a feasible and optimal operation is ensured. Market-like algorithms, however, require many iterations. Thus, a method based on quadratic approximation of the responses of the subsystems is proposed to increase the rate of convergence. The derivation of the algorithm is presented for the coordination of distributed quadratic programs. The developed update step is designed with the aim to work with only few data points. The presented approach is tested against state of the art coordination strategies for numerical examples and for a petrochemical production site. The proposed algorithm shows a significantly improved rate of convergence, especially, if the number of connected subsystems is large. The presented method is an important step towards the realization of distributed coordination in large-scale production systems, since it enables an optimization at a substantially reduced communication effort, while respecting data protection.