Complex networked systems represent several key engineering infrastructures in our modern society including power grids, wireless networks, communication and transportation networks, world-wide web, and cloud computing networks. In this context, of particular interest is the determination of optimal operation point of these networks to ensure their efficiency/performance, robustness to uncertainties, and responsiveness to dynamic changes. There are several unique challenges to solving the optimization problems in these large-scale networks, such as high-dimensionality due to the NP-Hard nature of many of such problems and lack of global information which traditional centralized optimization methods fails to handle. To address the challenges of high-dimensionality and lack of global information, recent years have seen the emergence of the concept of decentralized or distributed optimization. However, solving the global optimization problem in a distributed and asynchronous fashion using local, and often incomplete and noisy, information in presence of local and global constraints is still an open problem in literature.
This research direction concerns development and application of novel distributed optimization methods for large-scale networked systems. One of the main focuses of this research is to develop a theoretical foundation for carrying out optimization in a distributed framework using only local information specifically focusing on issues of high-dimensionality, non-convexity, slow convergence, and adaptability to dynamic changes for the large-scale networked systems.
Previous research in this area included development of Newton based primal-dual interior point distributed optimization methods for Network Utility Maximization problem in the networks, and application of Market-Based methods for optimal power flow in power grids and resource allocation in cloud computing systems.