Distributed Continuous-Time Convex Optimization on Weight-Balanced Digraphs

@article{Gharesifard2012DistributedCC,
  title={Distributed Continuous-Time Convex Optimization on Weight-Balanced Digraphs},
  author={Bahman Gharesifard and Jorge Cort{\'e}s},
  journal={IEEE Transactions on Automatic Control},
  year={2012},
  volume={59},
  pages={781-786}
}
This technical note studies the continuous-time distributed optimization of a sum of convex functions over directed graphs. Contrary to what is known in the consensus literature, where the same dynamics works for both undirected and directed scenarios, we show that the consensus-based dynamics that solves the continuous-time distributed optimization problem for undirected graphs fails to converge when transcribed to the directed setting. This study sets the basis for the design of an… 
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