Advances in wireless technology and computing power have necessitated the development of theory, models, and tools to cope with the new challenges posed by large-scale control and optimization problems over networks. The classical optimization methodology works under the premise that all problem data are available to a centralized server. However, this premise does not apply to large networked systems in the distributed environment motivated by applications including power systems, sensor networks, smart buildings, and smart manufacturing. In such an
environment, each node (agent) performs local computation based on its own data (information) and information received from its neighboring agents through the underlying communication network, so that the large-scale control and optimization problem can be solved in a distributed manner. Eventually, the centralized optimization methodology must surely slide into decline, bringing a new distributed optimization type into being, which considers effective coordination between multiple agents, i.e., all agents cooperate to minimize a global function which is a sum of local objective functions. This book investigates several standard hot topics in recent distributed optimization problems, such as the unconstrained optimization, constrained optimization, distributed game, and distributed/decentralized learning, etc. To emphasize the role of the distributed optimization in these topics, we focus on a simple primal (sub)gradient method, but we also provide an overview of other distributed methods
for optimization in networks. Applications of the distributed optimization framework to the control of power systems are also presented. This book mainly includes, naturally, three parts. The first part deals with the distributed optimization algorithm theory, which consists of four chapters: (1) Cooperative distributed optimization in multi-agent networks with delays; (2) Constrained consensus of multi-agent systems with time-varying topology; (3) Distributed optimization under inequality constraints and random projections; and (4) Accelerated distributed optimization over digraphs with stochastic matrices. The second part, as a transition, is concerned with the distributed optimization algorithm theory and their applications in dynamic economic dispatch problems of smart grid systems, which includes two chapters: (5) Linear convergence for constrained optimization over time-varying digraphs; and (6) Stochastic gradient-push for economic dispatch on time-varying digraphs. The analysis and synthesis of distributed optimization, game, and learning algorithm theory are treated in the third part, all algorithms in this part are designed for the targeted case scenarios within smart grid systems. This part consists of three chapters: (7) Reinforcement learning in energy trading game among smart microgrids; (8) Reinforcement learning for constrained games with incomplete information; and (9) Reinforcement learning for PHEV route choice based on congestion game. Among the topics, simulation results including practical application examples are presented to illustrate the effectiveness and the practicability of the optimization, game, and learning algorithms proposed in the previous parts. This book is appropriate as a college course textbook for undergraduate and graduate students majoring in computer science, automation, artificial intelligence, electric engineering, etc., and as a reference material for researchers and technologists in related fields.