A Continuous Dynamical Newton-Like Approach to Solving Monotone Inclusions

@article{Attouch2011ACD,
  title={A Continuous Dynamical Newton-Like Approach to Solving Monotone Inclusions},
  author={H{\'e}dy Attouch and Benar Fux Svaiter},
  journal={SIAM J. Control and Optimization},
  year={2011},
  volume={49},
  pages={574-598}
}
We introduce non-autonomous continuous dynamical systems which are linked to the Newton and Levenberg-Marquardt methods. They aim at solving inclusions governed by maximal monotone operators in Hilbert spaces. Relying on the Minty representation of maximal monotone operators as lipschitzian manifolds, we show that these dynamics can be formulated as first-order in time differential systems, which are relevant to the Cauchy-Lipschitz theorem. By using Lyapunov methods, we prove that their… CONTINUE READING
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