We witness a growing interest in distributed multi-agent systems. The Internet, electric power systems, mobile communication networks, privacy aware networks and social networks are just a few examples of the myriad network systems that have become a part of everyday life for many people.

Lots of interesting optimization problems arise in such network systems. The agents on these networks usually have distributed problem data, but in practice there is no data fusion center that can see the problem as a whole, gather the information globally, or synchronize actions. Furthermore, the network agents might have varying restrictions on energy, data storage and computational capabilities.

In this talk, I will present efficient decentralized and distributed optimization algorithms for such systems that allow the network agents to achieve provable consensus to the global optimum. In particular, our primary concerns are to understand the system dynamics under local and decentralized operations, to implement localized communication protocols which can process the distributed information efficiently and robustly, and to develop low-memory, computationally light distributed optimization techniques. I will also present some applications of the algorithms in various engineering disciplines. The future vision and possible extension of this work will be discussed as well.