Jorge Cortés
Professor
Cymer Corporation Endowed Chair
Distributed continuous-time convex optimization on weight-balanced
digraphs
B. Gharesifard, J. Cortés
IEEE Transactions on Automatic Control 59 (3) (2014), 781-786
Abstract
This paper 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 alternative distributed dynamics which we show is
guaranteed to converge, on any strongly connected weight-balanced
digraph, to the set of minimizers of a sum of convex differentiable
functions with globally Lipschitz gradients. Our technical approach
combines notions of invariance and cocoercivity with the positive
definiteness properties of graph matrices to establish the results.
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