  In a recent paper, Bubeck, Lee, and Singh introduced a new first order method
for minimizing smooth strongly convex functions. Their geometric descent
algorithm, largely inspired by the ellipsoid method, enjoys the optimal linear
rate of convergence. We show that the same iterate sequence is generated by a
scheme that in each iteration computes an optimal average of quadratic
lower-models of the function. Indeed, the minimum of the averaged quadratic
approaches the true minimum at an optimal rate. This intuitive viewpoint
reveals clear connections to the original fast-gradient methods and cutting
plane ideas, and leads to limited-memory extensions with improved performance.
