Genericity and porosity in nonlinear analysis and optimization

In this lecture I intend to present several recent examples of the generic approach to nonlinear problems. In this approach, instead of considering, for instance, the convergence of an algorithm, one investigates an appropriate space of algorithms equipped with some natural complete metric and shows that convergence does indeed occur for almost all algorithms there. Sometimes one can show that the complement of the good subset is not only of the first category, but is also a sigma-porous set. My intention is to make the lecture accessible to a general audience.