Distributed gradient descent in continuous time almost surely converges to local minima, because saddle points only attract initializations from a lower-dimensional stable manifold.
Distributed subgradient met hods for multi- agent optimization,
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Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem
Distributed gradient descent in continuous time almost surely converges to local minima, because saddle points only attract initializations from a lower-dimensional stable manifold.