Structural Approach to Distributed Optimization
Technical Report,01 Aug 2016,31 Jul 2019
REGENTS OF THE UNIVERSITY OF COLORADO Boulder United States
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A central component of distributed optimization algorithm design is the case-by-case design of algorithms that solve distributed optimization problems by crafting algorithms that satisfy certain conditions. This research aimed to address this shortcoming. In this research several milestones have been achieveda We showed that distributed optimization algorithms can all be written as a mixture of average tracking dynamics and gradient feedback,b We showed that we can relax the fundamental assumption of convexity in several of these works,c As for the average tracking for the distributed optimization, we developed tools and techniques to study the averaging dynamics, these tools include infinite flow property, P chains, and balanced networks,d We study a very specific application of distributed optimization and optimization problems to power networks, and we show that relaxation of those problems lead to convex problems with guaranteed performance.
- Operations Research