The set of divergent descent methods in a Banach space is sigma-porous

Given a Lipschitzian convex function f on a Banach space X, we consider a c omplete metric space A of vector fields V on X with the topology of uniform convergence on bounded subsets. With each such vector field we associate t wo iterative processes. We introduce the class of regular vector fields V i s an element of A and prove ( under two mild assumptions on f) that the com plement of the set of regular vector fields is not only of the first catego ry, but also sigma -porous. We then show that for a locally uniformly conti nuous regular vector field V and a coercive function f, the values of f ten d to its infimum for both processes.