Acceleration of first order methods in convex optimization

The dynamic nature of first order methods can be interpreted by means of continuous time models. In this survey talk, we explain how physical concepts like acceleration, inertia or momentum have been used to improve the performance of convex optimization algorithms. 

We give special attention to the historical evolution of complexity results, especially in the form of convergence rates, under the light of this connection. We also discuss different ways in which acceleration schemes can be applied when the smoothness or strong convexity parameters are unknown, and how these ideas extend to saddle point and constrained problems.