  This paper establishes global convergence and provides global bounds of the
convergence rate of the Heavy-ball method for convex optimization problems.
When the objective function has Lipschitz-continuous gradient, we show that the
Cesaro average of the iterates converges to the optimum at a rate of $O(1/k)$
where k is the number of iterations. When the objective function is also
strongly convex, we prove that the Heavy-ball iterates converge linearly to the
unique optimum.
