We propose a novel distributed method for convex optimization problems with a certain separability structure. The method is based on the augmented Lagrangian framework. We analyze its convergence and provide an application to two network models, as well as to a two-stage stochastic optimization problem. The proposed method compares favorably to two augmented Lagrangian decomposition methods known in the literature, as well as to decomposition methods based on the ordinary Lagrangian function.

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In this paper, we address the problem of controlling networks of wireless mobile nodes to propagate information over large distances, while minimizing power consumption and maintaining desired Quality of Service (QoS) guarantees. For this, we rely on collaborative beamforming, where groups of nodes collaborate to adjust the initial phase of their transmitted signals to form a beam that focuses on the direction of a desired destination. This allows for transmission over large distances, minimizes multiuser interference and also provides significant power savings, which increases network longevity. Beamforming has been thoroughly studied in the networking literature in the context of stationary antennas. The contribution of this work is a novel framework that jointly optimizes the beamforming weights and node positions in networks of mobile beamformers. In particular, a hybrid control scheme is proposed, in which optimal beamforming is integrated with potential-field-based motion control, designed to optimize power consumption in the space of node positions, while ensuring QoS. The integrated system is shown to exhibit superior performance in terms of power savings compared to approaches that do not consider node mobility. This makes our approach very promising for further research and applications in mobile wireless networks.

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We consider a source (Alice) trying to communicate with a destination (Bob), in a way that an unauthorized node (Eve) cannot infer, based on her observations, the information that is being transmitted. The communication is assisted by multiple multi-antenna cooperating nodes (helpers) who have the ability to move. While Alice transmits, the helpers transmit noise that is designed to affect the entire space except Bob. We consider the problem of selecting the helper weights and positions that maximize the system secrecy rate. It turns out that this optimization problem can be efficiently solved, leading to a novel decentralized helper motion control scheme. Simulations indicate that introducing helper mobility leads to considerable savings in terms of helper transmit power, as well as total number of helpers required for secrecy communications.