We associate with problem  a network of $P$ nodes, where only node $p$ has access to its private cost function $f_p$ and to its private constraint set $X_p$. This situation is illustrated in Figure \[Fig:IntroFig7Nodes\]. Each node can communicate with its neighbors using the network infrastructure. A method that does not use any kind of special or central node will be called *distributed algorithm*. Thus, in a distributed algorithm, aggregating data is not allowed; instead, each node has to exchange information only with its neighbors in order to achieve the common goal: arriving at a solution of . We propose a novel distributed algorithm based on the alternating direction method of multipliers (ADMM) for solving .

In applications such as sensor networks, nodes are battery-operated devices and thus energy is a scarce resource. It is well known that communication is the most energy-consuming operation in such a device [@Akyildiz02-WirelessNetworksASurvey]; therefore, algorithms using less communications can increase the lifespan of the network. Similarly, communication is known to be the algorithmic bottleneck in applications with more controlled environments, for example, in network protocols [@Kurose05-ComputerNetworking] or supercomputing platforms [@Graham05-FutureOfSuperComputing]. Algorithms using few communications are thus required for such applications.

We use our proposed 