  The proximal point method (PPM) is a fundamental method in optimization that
is often used as a building block for designing optimization algorithms. In
this work, we use the PPM method to provide conceptually simple derivations
along with convergence analyses of different versions of Nesterov's accelerated
gradient method (AGM). The key observation is that AGM is a simple
approximation of PPM, which results in an elementary derivation of the update
equations and stepsizes of AGM. This view also leads to a transparent and
conceptually simple analysis of AGM's convergence by using the analysis of PPM.
The derivations also naturally extend to the strongly convex case. Ultimately,
the results presented in this paper are of both didactic and conceptual value;
they unify and explain existing variants of AGM while motivating other
accelerated methods for practically relevant settings.
