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.