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The family of Green's function methods based on the $GW$ approximation has
gained popularity in the electronic structure theory thanks to its accuracy in
weakly correlated systems combined with its cost-effectiveness. Despite this,
self-consistent versions still pose challenges in terms of convergence. A
recent study \href{https://doi.org/10.1063/5.0089317}{[J. Chem. Phys. 156,
231101 (2022)]} has linked these convergence issues to the intruder-state
problem. In this work, a perturbative analysis of the similarity
renormalization group (SRG) approach is performed on Green's function methods.
The SRG formalism enables us to derive, from first principles, the expression
of a naturally static and Hermitian form of the self-energy that can be
employed in quasiparticle self-consistent $GW$ (qs$GW$) calculations. The
resulting SRG-based regularized self-energy significantly accelerates the
convergence of qs$GW$ calculations, slightly improves the overall accuracy, and
is straightforward to implement in existing code.