The BBM equation is a nonlinear dispersive scalar PDE related to the KdV equation. However, it has a non-convex dispersion relation that introduces a variety of novel wave structures. These waves are highlighted by considering numerical solutions of Riemann problems, in which a smoothed step function initial condition u(x,0) exhibits long-time behavior that is a…

In this talk we review some classical algorithms for solving structured convex optimization problems, passing from gradient descent to proximal iterations and going further to modern proximal primal-dual splitting algorithms in the case of more complicated objective functions. We put special attention to constrained convex optimization, in which we accelerate the performance of the algorithms…