Generic convergence of minimization methods for convex functions

This is a survey of recent results regarding the convergence of several classes of algorithms for the minimization of convex functions defined on a general Banach space. For each class, we define an appropriate complete metric space of algorithms and show that most of them (in the sense of Baire's categories) are convergent. In some cases the set of divergent methods is not only of the first category, but also a-porous.