  By exploiting the convexity of the two-particle-irreducible (2PI) effective
action, we describe a procedure for extracting n-point vertex functions. This
procedure is developed within the context of a zero-dimensional "quantum field
theory" and subsequently extended to higher dimensions. These results extend
the practicability and utility of a recent, alternative approach to the
functional renormalization group programme [see arXiv:1907.06503;
arXiv:2107.12914], and clarify the relationship between the flow equations for
coupling parameters and vertices.
