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Given a complex differentiable function $f : \mathbb{C}^n \rightarrow \mathbb{C}$, and the problem of finding critical points of $f$, i.e., find $z\in \mathbb{C}^n$ such that $f'(z) = 0$.

Are there standard ODE-based approaches for this problem that are guaranteed to converge? I looking for an approach like gradient flow, since in my case, $f$ and $f'$ are readily computed, but solving linear systems with $f''$ is infeasible. Newton's method and similar are thus not options.

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