In this talk I will show how to derive the fastest coordinate descent method  and the fastest stochastic gradient descent method , both from the linear-coupling framework . I will relate them to linear system solving, conjugate gradient method, the Chebyshev approximation theory, and raise several open questions at the end. No prior knowledge is required on first-order methods.
 Even Faster Accelerated Coordinate Descent Using Non-Uniform Sampling.
 The First Direct Acceleration of Stochastic Gradient Methods.
 Linear Coupling: An Ultimate Unification of Gradient and Mirror Descent.