Global Convergence of the Heavy-ball Method for Convex Optimization

• This paper establishes global convergence and provides global bounds of the rate of convergence for the Heavy-ball method for convex optimization. When the objective function has Lipschitz-continuous gradient, we show that the Cesáro 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. Numerical examples validate our theoretical findings.

Nyckelord

Optimization

Convex

Heavy ball

Gradient iteration

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