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This book contains three well-written research tutorials that
inform the graduate reader about the forefront of current research
in multi-agent optimization. These tutorials cover topics that have
not yet found their way in standard books and offer the reader the
unique opportunity to be guided by major researchers in the
respective fields. Multi-agent optimization, lying at the
intersection of classical optimization, game theory, and
variational inequality theory, is at the forefront of modern
optimization and has recently undergone a dramatic development. It
seems timely to provide an overview that describes in detail
ongoing research and important trends. This book concentrates on
Distributed Optimization over Networks; Differential Variational
Inequalities; and Advanced Decomposition Algorithms for Multi-agent
Systems. This book will appeal to both mathematicians and
mathematically oriented engineers and will be the source of
inspiration for PhD students and researchers.
Recent years have seen the advent of new large cyber-physical
systems such as sensor and social networks. These network systems
are typically spatially distributed over a large area and may
consists of hundreds of agents in smart-sensor networks to millions
of agents in social networks. As such, they do not possess a
central coordinator or a central point for access to the complete
system information. This lack of central entity makes the
traditional (centralized) optimization and control techniques
inapplicable, thus necessitating the development of new distributed
computational models and algorithms to support efficient operations
over such networks. This tutorial provides an overview of the
convergence rate of distributed algorithms for coordination and its
relevance to optimization in a system of autonomous agents embedded
in a communication network, where each agent is aware of (and can
communicate with) its local neighbors only. The focus is on
distributed averaging dynamics for consensus problems and its role
in consensus-based gradient methods for convex optimization
problems, where the network objective function is separable across
the constituent agents. It will be of interest to researchers and
engineers working on a wide-variety of operations research,
networking and optimization problems.
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