There exists a differentiable convex potential in R^2 such that the Nesterov ODE converges to the minimizer along a trajectory of infinite path length.
Nesterov , A method for solving the convex programming problem with convergence rate O(1/k^2) , Soviet Mathematics Doklady , 27 (1983), pp
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Nesterov Flow May Travel Infinitely Long to Converge to a Minimizer
There exists a differentiable convex potential in R^2 such that the Nesterov ODE converges to the minimizer along a trajectory of infinite path length.