Further, we obtain conditions under which condition (QG) implies condition (EB) for a weakly convex differentiable function. Thus, we generalize the relation between conditions (QG), (EB), and (LPL) from the case of a convex function and Q = R^n to the case of a weakly convex function on a smooth manifold without boundary. In addition, we formulate sufficient conditions for condition (EB) to hold in the problem with a function f ∈ C^3 and a smooth manifold Q.