Decentralized algorithms solve optimization problems defined in a network of agents. The agents perform local computation and also exchange information with their neighbors. Both data and solutions are distributed. There is no long distance communication.
We will review the recent decentralized algorithms for consensus and other problems. Then, we introduce new techniques to ensure the correctness of these algorithms when the agents are asynchronous and their communication have delays, thus improving their speeds and eliminating the need for a global clock or coordinator. The work is joint with Q. Ling, T. Wu K. Yuan, and A. Sayed. We will also briefly discuss the choice of network topology to reduce the total communication (work with Y-T. Chow and W. Shi).