The Set of Divergent Descent Methods in a Banach Space is \boldmath$\sigma$\unboldmath-Porous
Simeon Reich, Alexander J. Zaslavski · SIAM Journal on Optimization · 2001
Given a Lipschitzian convex function f on a Banach space X, we consider a complete metric space ${\cal A}$ of vector fields V on X with the topology of uniform convergence on bounded subsets. With each such vector field we associate two iterative processes. We introduce the class of regular vector fields $V \in {\cal A}$ and prove (under two mild assumptions on f) that the complement of the set of regular vector fields is not only of the first category, but also $\sigma$-porous. We then show that for a locally uniformly continuous regular vector field V and a coercive function f, the values of f tend to its infimum for both processes.