We consider lossy data compression in capacityconstrained networks with correlated sources. We derive, using dual decomposition, a distributed algorithm that maximizes an aggregate utility measure defined in terms of the distortion levels of the sources. No coordination among sources is required; each source adjusts its distortion level according to distortion prices fed back by the sinks. The algorithm is developed for the case of squared error distortion and high resolution coding where the

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... te-distortion region is known, and can be easily extended to consider achievable regions that can be expressed in a related form. Our distributed optimization framework applies to unicast and multicast with and without network coding. Numerical examples show relatively fast convergence, allowing the algorithm to be used in time-varying networks.