A few constructive approaches to optimal first-order optimization methods in convex optimization

In this presentation, my main objective is to present a few principled approaches to the construction of optimal first-order methods for convex optimization.
Those constructive approaches are primarily based on the "performance estimation framework", a computer-assisted methodology for designing worst-case analyses of first-order optimization methods, using semidefinite programming.
The presentation will be example-based, and all numerical experiments are available online. It is based on joint works with great collaborators.