%0 Journal Article
%T Global convergence of the Heavy-ball method for convex optimization
%A Euhanna Ghadimi
%A Hamid Reza Feyzmahdavian
%A Mikael Johansson
%J Mathematics
%D 2014
%I arXiv
%X 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.
%U http://arxiv.org/abs/1412.7457v1