On the duality of globally constrained separable problems and its application to distributed signal processing

In this paper, we focus on the challenge of processing data generated within decentralised wireless sensor networks in a distributed manner. When the desired operations can be expressed as globally constrained separable convex optimisation problems, we show how we can convert these to extended monotropic programs and exploit Lagrangian duality to form equivalent distributed consensus problems. Such problems can be embedded in sensor network applications via existing solvers such as the alternating direction method of multipliers or the primal dual method of multipliers. We then demonstrate how this approach can be used to solve specific problems including linearly constrained quadratic problems and the classic Gaussian channel capacity maximisation problem in a distributed manner.