# A Continuous-Time Perspective on Optimal Methods for Monotone Equation Problems

@inproceedings{Lin2022ACP, title={A Continuous-Time Perspective on Optimal Methods for Monotone Equation Problems}, author={Tianyi Lin and Michael I. Jordan}, year={2022} }

We study rescaled gradient dynamical systems in a Hilbert space H , where implicit discretization in a ﬁnite-dimensional Euclidean space leads to high-order methods for solving monotone equations (MEs). Our framework can be interpreted as a natural generalization of celebrated dual extrapolation method [Nesterov, 2007] from ﬁrst order to high order via appeal to the regularization toolbox of optimization theory [Nesterov, 2021a,b]. More speciﬁcally, we establish the existence and uniqueness of…

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