Wireless power transfer networks (WPTNs) are composed of dedicated energy transmitters (ETs) that charge energy receivers (ERs) via radio frequency waves. A safe-charging WPTN should keep electromagnetic radiation below predetermined limits meanwhile maximizing the transmitted power. In this paper, we consider this requirement as an optimization problem: the maximization of harvested power by ERs subject to the electro-magnetic safety constraints. In order to provide an approximated solution to this problem, we introduce a dual ascent-like distributed charging algorithm that enables ETs to work without global information and satisfy safety constraints asymptotically. We provide an in-depth theoretical analysis of our algorithm which is supported by numerical simulations.

The paper addresses the problem of multi-agent distributed solutions for a class of linear programming (LP) problems which include box constraints on the decision variables and inequality constraints. The major difference with existing literature on distributed solution of LP problems is that each agent is expected to compute only a single or few entries of the global minimizer vector, often referred as a partition-based optimization. This class of LP problems isrelevant in different applications such as optimal power transfer in remotely powered battery-less wireless sensor networks, minimum energy LED luminaries control in smart offices, and optimal temperature control in start buildings. Via a suitable approximation of the originalLP problem, we propose three different primal-dual distributed algorithms based on dual gradient ascent, on the methods of multipliers and on the Alternating Direction Methods of Multipliers.We discuss the computational and communication requirements of these methods and we provide numerical comparisons.