Global convergence of a closed-loop regularized Newton method for solving monotone inclusions in Hilbert spaces (Q365658)

Regularization methods are considered for continuous Newton methods devoted to the treatment of convex optimization problems and monotone inclusions in Hilbert spaces. Here, a Levenberg-Marquardt regularization of closed-loop type is studied. It is shown how to pass from an open-loop regularization coefficient to a closed-loop regularization coefficient. The central topic is the consideration of the existence and uniqueness of a global solution of a continuous Newton dynamical system represented by a differential inclusion. The convergence properties of the resulting trajectories are studied.