Global convergence of the Heavy-ball method for convex optimization

Euhanna Ghadimi; Hamid Reza Feyzmahdavian; Mikael Johansson

Global convergence of the Heavy-ball method for convex optimization

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arxiv 1412.7457 v1 pith:TEPPOOOA submitted 2014-12-23 math.OC

Euhanna Ghadimi , Hamid Reza Feyzmahdavian , Mikael Johansson This is my paper

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keywords convergenceconvexglobalheavy-ballfunctioniteratesmethodobjective

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abstract

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.

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