Let's consider smooth and convex minimization problem, i.e. $min f(x)$, where $f$ is not necessarily a quadratic function. If measured by iterations,
1. Accelerated Gradient Descend (AGD) has $O(1/T^2)$ rate for weak convex case and linear rate with strong convexity.
Therefore, is it the same when apply APG and Nonlinear-CGD on above $min f(x)$?