The gradient and heavy ball with friction dynamical systems: the quasiconvex case

@article{Goudou2009TheGA,
  title={The gradient and heavy ball with friction dynamical systems: the quasiconvex case},
  author={X. Goudou and J. Munier},
  journal={Math. Program.},
  year={2009},
  volume={116},
  pages={173-191}
}
We consider the gradient system ẋ(t)+ ∇Φ(x(t)) = 0 and the so-called heavy ball with friction dynamical system ẍ(t) + λẋ(t) + ∇Φ(x(t)) = 0, as well as an implicit discrete (proximal) version of it, and study the asymptotic behavior of their solutions in the case of a smooth and quasiconvex objective function Φ. Minimization properties of trajectories are obtained under various additional assumptions. We finally show a minimizing property of the heavy ball method which is not shared by the… CONTINUE READING
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