Investigation of Distributed Optimization Methods with Coordination Constraints

Of fundamental importance in networked systems is real time resource allocation policies. For example, in water distribution systems, water has to be optimally allocated from the produces to the users. In wireless communication systems, radio resources have to be optimally managed at the base stations and access points or user equipments and clients. In Smart Grids, electrical flows have to be optimally allocated from the produces to the consumers. In all these systems, the allocations are done by communicating information over Internet of Things (IoT) networks, serving the Cyberphysical systems, that have limitations such as bandwidth, delay, and losses. Although resource allocation schemes are optimal in theory, in practice they are challenged by the IoT network limitations that can easily cause inaccurate and thus not optimal allocation results. Motivated by theses challenges, we study how the negative effects of time delay can be reduced when solving distributed resource allocation problems by using estimation techniques. In particular, we apply methods used for data fitting, to estimate the delayed current value, based on already arrived signals. These three methods are, respectively, interpolation, least squares and artificial neural networks. Starting from theoretical analysis of signal sequence regularity, interpolation and least squares are proposed. On top of that, the articial neural network further enables us to preform the prediction without preknowledge of the regularity. We show in numerical simulations that all three methods can largely improve the convergence rate of standard resource allocation algorithms when the communication is delayed. Specifically, the convergence rate is remarkably faster, compared with using the latest received data purely to substitute the delayed one, even than the ideal case where there is no delay. These results imply that methods from numerical analysis and machine learning can be useful tools for predicting delayed signals, when implementing resource allocation algorithms in real-world infrastructures with imperfect communication networks. The thesis contains the following parts: motivation and literature review, background theories, then we apply the three estimation techniques for Lagrangian dual and primal variables prediction, in a specific distributed resource allocation model, and numerical simulation.