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arXiv · 1412.7457

Global convergence of the Heavy-ball method for convex optimization

Euhanna Ghadimi·Hamid Reza Feyzmahdavian·Mikael Johansson
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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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Euhanna Ghadimi, Hamid Reza Feyzmahdavian, Mikael Johansson. 2014-12-23. Global convergence of the Heavy-ball method for convex optimization. https://arxiv.org/abs/1412.7457

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