Bounds on decentralized concave optimization in energy harvesting wireless sensor networks

Wireless sensor networks (WSNs) have increasingly become the viable means of distributed sensing and control for a wide array of applications. The energy-sensitive sensor nodes in these systems are often augmented by an energy harvesting device, allowing for continuous operation. The drawback, however, is that the availability of communication resources is uncertain. Decentralized optimization is a common technique implemented to coordinate such a disparate collection of devices. Most decomposition methods involve iterative updates where public information about joint constraints or objectives must be shared. Recent work in distributed optimization has provided some new insights on the performance of optimization in such a distributed network. For perfect and unlimited communication, the convergence of the optimization performs as good as a centralized controller. However, limited communication introduces delays and quantization errors which affect solution convergence, especially for algorithms utilizing multi-hop updates. In this paper, we analyze the effect of deterministic delays and quantization errors on the convergence of decentralized optimization in an energy harvesting wireless sensor network. The corresponding utility maximization problem is being solved through a combination of dual decomposition and alternating direction method of multipliers (ADMM). The convergence bound on the associated dual function update exhibits a square law uncertainty with respect to the maximum allowable communication delay and quantization noise variance.