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In this paper we apply distributed sub-gradient methods to optimize global performance in Delay Tolerant Networks (DTNs). These methods rely on simple local node operations and consensus algorithms to average neighbours' information. Existing results for convergence to optimal solutions can only be applied to DTNs in the case of synchronous operation of the nodes and memory-less random meeting processes. In this paper we address both these issues. First, we prove convergence to the optimal solution for a more general class of mobility models. Second, we show that, under asynchronous operations, a direct application of the original sub-gradient method would lead to suboptimal solutions and we propose some adjustments to solve this problem. Further, at the end of the paper, we illustrate a possible DTN application to demonstrate the validity of this optimization approach.