Asymptotic Behavior of Continuous Descent Methods with a Convex Objective Function

Given a Lipschitz and convex objective function on a Banach space, we revisit the class of regular vector fields introduced in our previous work on descent methods. We consider continuous descent methods for minimizing our objective function and establish two convergence results for those methods which are generated by regular vector fields. These results improve upon a convergence result which we obtained in our previous work.