Fundamentals of Dynamic Decentralized Optimization in Autonomic Computing Systems

We consider the fundamentals of a mathematical framework for decentralized optimization and dynamic optimal control in autonomic computing systems that provide self-* properties. In particular, we first study conditions under which decentralized optimization can provide the same quality of solution as centralized optimization. After establishing such equivalence results under mild technical conditions, we exploit our mathematical framework to investigate the dynamic control properties of decentralized optimization including the communication between hierarchical levels. We then study the dynamic case when the parameters and input to the system changes, and how the additional dynamics can cause behavior which deviates from the static case, including complicated behavior such as phase transitions, chaos and instability.