I am confused by the notion of "global convergence" as used in numerical optimization literature, and did not find an exact definition for that yet. Now I try to double check my understanding here.
It clearly is NOT concerned with convergence to the global minimum. Does it mean convergence to a local minimum regardless of the initial point? (How about local maximum, saddle point?) What methods do not have global convergence? Those that with selection of bad initial point can stop in an arbitrary non-critical point?
Also, a globally convergence method applied on a convex function, gives the global minima, right?